how to find quadratic equation from points how to find quadratic equation from points

Substituting 2 for h and 3 for k into, Substitute the point's coordinates for x and y in the equation. They can be used to calculate areas, formulate the speed of an object, and even to determine a product's profit. First note, Posted 9 years ago. i.e a trinomial? [] Bourne of squareCircleZ has posted onHow to find the equation of a quadratic function from its graph. Use the given point (-1, 3), which says y is 3 for x equal to -1. System of Equations method; The equation that describes the graph with points (1, 5), (2, 11) and (3, 19) is x^2 + 3x + 1. A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. * E-Mail (required - will not be published), Notify me of followup comments via e-mail. Direct link to Adithi J's post Good question! If you mean it's a parabola, the systems of equations method as given in the post works whether the parabola passes through the x-axis or not. You could post it somewhere (e.g. I am a 41 year old who is about to study maths and physics at uni for the first time; stuff like this is fantastic. Use the given point (-1, 3), which says y is 3 for x equal to -1. This helps a lot!!! @Simon: You'll need to use the "Vertex Method" as detailed in the article. So long asa0, you should be able to factor the quadratic equation. GeoGebra is the way to go, I believe. . Suppose yourbis positive; the opposite is negative. Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale athttp://mariosmathtutoring.teachable.comFor online 1-to-1 tutoring or more information about me see my website at:http://www.mariosmathtutoring.com* Organized List of My Video Lessons to Help You Raise Your Scores \u0026 Pass Your Class. I am transport planning student and have lot of data where i have to fit parabola. It's near (0.5, 3.4), but "near" will not give us a correct answer. This means that at no point will. @Peter: Actually, if there are 3 intercepts, it's a quadrinomial. Please reply soon. 2021-11-06 Added 102 answers. This gives us y = a(x 1)2. the curve will have an absolute maximum). Do you mind if I quote a few of your articles as long as I provide credit and sources back to your blog? @Mathan: What kind of "curve" are you talking about? The expression b24ac{b}^{2}-4acb24ac, which is under the(sqrt) inside the quadratic formula is called the discriminant. May God bless and guide you! If you need to cheat in a math test, use this app. This app is simply amazing. Hopefully this proof helps you understand why: There are several ways to derive the quadratic formula, but the simplest is by using completing the square. Therefore Try not to think of-bas"negativeb" but as theoppositeof whatever value"b"is. Given just 2 points, to find a linear equation, this is the formula: $$y\ =\frac {\left (y_2-y_1\right)} {\left (x_2-x_1\right)}x+\frac {\left (y_1+y_2-\left (x_1\left (\frac {\left (y_2-y_1\right)} {\left (x_2-x_1\right)}\right)+x_2\left (\frac {\left (y_2-y_1\right)} {\left (x_2-x_1\right)}\right)\right)\right)} {2}$$ In the same form of How do i know when the curve goes like a u or a upside down u ? How do you solve those kinds? In an equation likeax2+bx+c=ya{x}^{2}+bx+c=yax2+bx+c=y, sety=0 and work out the equation. I'm having trouble in determining the equation from its graph (>.<) The image only has 5 units for each positive and negative x and y. Fitting a quadratic through 5 points, goal is to find the maximum. Then, see how find the value of that variable and use it to find the value of the other variable. I modified it to give a parabola with horizontal axis through your given 3 points. This app has been really great for helping me with my gcse work. The quadratic equation whose roots are , , is x 2 - ( + )x + = 0. The last ordered pair is (3, 19), which yields the equation: 19 = a(3^2) + 3(3) + 1. Google Photos) then put the link to it here. For instance, you can substitute (1, 5) into the equation to yield 5 = a(1^2) + b(1) + 1, which simplifies to a = -b + 4. A parabola is the locus of points equidistant from a How do you find exact values for the sine of all angles? Example Problems - Quadratic Equations Example 1 - solve with quadratic formula Example 2 - solve using Indian method Example 3 - solve by factoring Example 4 - completing the square Example 5 - create quadratic ALL Example Problems - Work Rate Problems Example 3 - time to wash cars Example 4 - Excel Linear Programming order now. Sign Up. Just go about it the same as I did int he article: start with y = ax^2 + bx + c and substitute in your 3 points, then solve. How could we go about figuring out the equation of other types of graphs? May be of interest to some of you, see this simple how-to obtain curve fitting equation from graph image / published graph at: https://pocketengineer.wordpress.com/2016/04/02/how-to-obtain-curve-fitting-equation-from-graph-image-published-graph/. In math, the meaning of square is an exponent to the second degree: So a quadratic polynomial has as its highest value something to the second degree; something squared. Concluding this example, squaring (x - 2) results in. Substituting 2 for h and 3. order now. Quadratic Equation in Standard Form: ax 2 + bx + c = 0 Quadratic Equations can be factored Quadratic Formula: x = b (b2 4ac) 2a When the Discriminant ( b24ac) is: positive, there are 2 real solutions zero, there is one real solution negative, there are 2 complex solutions Looking for detailed, step-by-step answers? A word with quad" in it usually implies four of something, like a quadrilateral. 3/9/10 5:45 AM. How to find the equation of a logarithm function from its graph? It only takes a minute to sign up. if you mean find the solution, yes, you would get -3 and 1. Thanks. NOTE: You can mix both types of math entry in your comment. using the amount of revenues and expenses, we can determine if based on the number of staff and encounters. Now, we can write our function for the quadratic as follows (since if we solve the following for 0, we'll get our 2 intersection points): This is a quadratic function which passes through the x-axis at the required points. For example, 11 = (-b - c + 5)(2^2) + b(2) + c simplifies to b = -1.5c + 4.5. This is a good question because it goes to the heart of a lot of "real" math. What if the curve not passing through any of axis. If you're seeing this message, it means we're having trouble loading external resources on our website. What if your originalbisalreadynegative? I do not enjoy math and I need some help. Now youve got the basics of the quadratic formula! That is one way to find a quadratic function's equation from its graph. To solve a quadratic equation, use the quadratic formula: x = (-b (b^2 - 4ac)) / (2a). find the equation of the tangents to a quadratic curve through the point $(-7,1)$ 1 Conic sections ( coordinates of the point of intersection of tangents with the curve ) I appreciate the simple images to go along with the explanations, that also helped a lot. Surround your math with. we are able to determine and establish goals. (If there are no other "nice" points where we can see the graph passing through, then we would have to use our estimate.). Substitute the vertex's coordinates for h and k in the vertex form. The average passing rate for this test is 82%. Quadratic Equation Solve by Factoring Calculator, Quadratic Equation Completing the Square Calculator, Quadratic Equation using Quadratic Formula Calculator. The best thing is to supply the question and an example given by the teacher so I can see what they mean. Why is this the case. We will now prepare a table for the roots of "X" which are "x1" and "x2", and . instead of the formula, my textbook wants me to use factorization..how to i do x^2+2x-3=0? Just as a quadratic equation can map a parabola, the parabola's points can help write a corresponding quadratic equation. Use the calculator to verify the rounded results, but expect them to be slightly different. Substitute the third ordered pair and the values of a and b into the general equation. Just give me a few minutes and I'll have the answer for you. We can see on the graph that the roots of the quadratic are: x = 2 (since the graph cuts the x-axis at x = 2); and, x = 1 (since the graph cuts the x-axis at x = 1.). Point A (|) Point B (|) Point C (|) if we fit these points generally they fit on parabola with axis of symmetry on Y axis but i want to fit these points in parabola with axis of symmetry on X Axis and 2 points of the parabola intersecting on Y Axis. This is the perfect place to come for a walk or a run, with a wide track that is well maintained. She holds a Bachelor of Science in cinema and video production from Bob Jones University. Quadratic equation standard form. Direct link to Estelle Pretorius's post If the coefficient of x^2, Posted 5 years ago. Good luck with your studies! @John: Yes, that would do it. It is written in the form: ax^2 + bx + c = 0 where x is the variable, and a, b, and c are constants, a 0. The vertex occurs where x = h, and that occurs at the lowest (or highest) y-value for your data. So the correct quadratic function for the blue graph is. Calculator Use. Math is a way of solving problems by using numbers and equations. For example, 11 = (-b + 4)(2^2) + b(2) + 1 simplifies to b = 3. I felt sick in Pre-Calc yesterday while they were reviewing this and wasn't up to asking the teacher to repeat everything cuz it didn't make sense at that moment but this really helps ! if b24ac=0{b}^{2}-4ac=0\to b24ac=0 1 solution, if b24ac>0{b}^{2}-4ac>0\to b24ac>0 2 solutions, if b24ac<0{b}^{2}-4ac<0\to b24ac<0 no real solution. Your work and problems are excellent. Final equation is: and i need to form a quadratic equation based on that could you pls help me out with it.. Hello Abhishek. Redoing the align environment with a specific formatting, Theoretically Correct vs Practical Notation. The square of a negative is a positive, sob2{b}^{2}b2will always be a positive value. Very well explained, I understood it well after reading it through once. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. How to find equation of quadratic function with two points - This site allow users to input a Math problem and receive step-by-step instructions on How to find. Direct link to nkfonseka's post Start from the beginning , Posted 7 years ago. The more data points you give Excel (especially near extremes like maxima, minima and x- and y-intercepts), the closer the resulting polynomial will be to your given graph. a is the height of the graph above that line at x=1. If you are trying to find the zeros for the function (that is find x when f(x) = 0), then that is simply done using quadratic equation - no need for math software. We can see the vertex is at (-2, 1) and the y-intercept is at (0, 2). of the parabola on the graph, and plug it into the vertex form of a quadratic equation. For example, placing theentirenumerator over2aisnotoptional. In order to find a quadratic equation from a graph, there are two simple methods one can employ: using 2 points, or using 3 points. One example (I found all of this on the cubic equation link) is the inverse of the function f(x)=x^5+x. Why do many companies reject expired SSL certificates as bugs in bug bounties? Good question! How to find the equation of a quadratic function from its graph, New measure of obesity - body adiposity index (BAI), Whats the Best? Local and online. Polynomials (algebraic expressions with many terms) can have linear, square, and cubic values. In this tutorial, you'll see how to solve such a system by combining the equations together in a way so that one of the variables is eliminated. @Adam: This would be a good question for the IntMath Forum. I hope it makes more sense now. To solve a quadratic equation, use the quadratic formula: x = (-b (b^2 - 4ac)) / (2a). Thanks, once again, for emphasizing "real" math (for both utility and understanding). Let's start with the simplest case. In solving quadratics, you help yourself by knowing multiple ways to solve any equation. By solving the algebraic equation, you have given yourself a head start on graphing the equation. 2 1 Sponsored by Forge of Empires Think of how much we know about our graph solution even before we perform any algebraic calculations: Since the equation will yield two solutions for x, we have two x-intercepts, We can start plotting the parabola with two ordered pairs, (x1,0)({x}_{1},0)(x1,0) and (x2,0)({x}_{2},0)(x2,0), The vertex of the parabola will be between the two x-intercepts. Kylene Arnold is a freelance writer who has written for a variety of print and online publications. Thanks. Consider a quadratic equation in standard form: a {x}^ {2}+bx+c=0 ax2 + bx + c = 0. What is the relationship between three points on a quadratic curve and the curves coefficients? Solve for a. The y -intercept is (0, -3). Mathepower calculates the quadratic function whose graph goes through those points. Instead of x, you can also write x^2. But on my math homework, I we are working with conic sections and parabolas. Step 1: Write the quadratic inequality in standard form. I love maths and as a maths student here in DWU university,this lesson send to me is a great help in my learning. We already have a quiz Mnday! Cheers everyone!! Direct link to Sam D's post Just curious, is there so, Posted 6 years ago. Hi, I found your explanation lucid and helpful. If you're looking for fast answers, you've come to the right place. Here's the appropriate section: https://www.intmath.com/forum/plane-analytic-geometry-37/, Please how can you find the equation of a quadratic curve when given only the plotted values. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic equation" as a synonym for quartic equation, others (Hazewinkel 1988, Gellert et al. For example, solving the equation for the points (0, 2) and (2, 4) yields: 2 = ab 0 and 4 = ab 2. Substituting for x and y: 3 = a(-1 - 3)2 - 1 = 3 = a(-4)2, Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola The axis of symmetry is x = 0 so h also, Find maximum of multivariable function calculator, Find the perimeter of an equilateral triangle of side 7cm, First order differential with initial value equation solver, How to find the area under the standard normal curve to the left of z, Intitial value differential equation solver, Rational expression calculator multiply and divide, Urge to pee at night but nothing comes out. Gimusi.Wonderful.I wish I could share anything with Lagrange. As the y intercept was at -3, could we not simply use this to determine the proper equation: If then And as we saw from the graph, the y-intercept is (0, -3). 1 - Enter the x and y coordinates of three points A, B and C and press "enter". I use this method to control the torque profile on a surface driven winder (real world math) The quadratic formula is: You can use this formula to solve quadratic equations. Another option could be to approach an existing entity that's doing interesting things (New York's Museum of Mathematics comes to mind) and offer your services as a researcher. I am to find a equation of a parablo given the vertex (7,-2) and one x-intercept (4,0). You can also try completing the square. Start solving a quadratic by seeing if it will factor (what two factors multiply to givecthat will also sum to giveb?). How to find the equation of that curve? y=\goldD {a} (x-\blueD h)^2+\greenD k y = a(x h)2 + k The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b (b^2 - 4ac)) / (2a). How did the value of a become 2? I can help you better if I can see your image. I am a physics and Maths student, and with this lesson sent to me is really a great help in doing quadratics and projectile motion. If all you knew was factoring, you would be stuck. With a simple review of your work, you can find ways to improve and understand How to find quadratic equation from two points! Ferrari was the first to develop an . Then a = 1, b = -7 and c = 10 Substitute them in the quadratic formula and simplify. Create the equations by substituting the ordered pair for each point into the general form of the quadratic equation, ax^2 + bx + c. Simplify each equation, then use the method of your choice to solve the system of equations for a, b and c. Finally, substitute the values you found for a, b and c into the general equation to generate the equation for your parabola. example http://www.sscc.edu/home/jdavidso/Math/Catalog/Polynomials/Fifth/FifthDegreeB.html how would I figure out the function? Method 1 Using the Vertex Formula 1 Identify the values of a, b, and c. In a quadratic equation, the term = a, the term = b, and the constant term (the term without a variable) = c. Posted in Mathematics category - 17 May 2011 [Permalink]. In the standard form Observe my graph passes through 3 on the y-axis. Where are we getting the 2 from and also why would we add it to the second line? More advanced: I want to fit parabola equation at any axis of symmetry. The locations produces a set of observations y for one value of x, the independent variable. I am a retired mathematics teacher at H.S and college level with a degree Substituting for x and y: 3 = a(-1 - 3)2 - 1 = 3 = a(-4)2. Hi, I might be seeming a bit stupid here, but how does 6a = 9 = 1.5? I was not aware of the FitPoly command in GeoGebra - it's a shame it is not included in one of the menus. The quadratic formula is used to solve quadratic equations. This will give you insight to the answer of @DrSonnhardGraubner. y = a(x r1)(x r2) If we specify r1 and r2, then we know exactly two points on this parabola, namely (r1,0), and (r2,0). Instead, you can derive the correct equation (#2) by merely multiplying #1 by 1.5, where 1.5 is the ratio of the correct constant term of -3 to the constant term of -2 in #1. If the coefficient of x^2 is positive, the curve will look like a u (i.e. Math is the study of numbers, shapes, and patterns. But there are an infinite number of parabolas that contain these two points because we can make the a coefficient any real number. For the b^2 part inside the square root, why can't it be transferred to the outside as b? GeoGebra was not so useful for this task. Enter the points in cells as shown, and get Excel to graph it using "X-Y scatter plot". The IntMath Forum would be the appropriate place for your question. Another approach to the parabola problem, which may be of particular interest to calculus students, is that for a parabola to be the graph of y=ax^2+bx+c: Substituting 3 for x and 8 for y in, Solve the equation for a. One such quadratic polynomial is f(x) = (x-1)(x-3, Popular culture quiz questions and answers, Quadratic equation jee mains previous year questions. If you need support, our team is available 24/7 . In the first two examples there is no need for finding extra points as they have five points and have zeros of the parabola. Thanks a lot! ), Although a rather long and drawn out discussion, it might be useful if you offered your readers the method for solving any order polynomial equation using matrix determinants and Cramer's rule. In this article, we review how to graph quadratic functions. Given just 2 points, to find a linear equation, this is the formula: It is derived from the Latin word quadrare, which means "to square", which is what you do in quadratics. If asked for the exact answer (as usually happens) and the square roots cant be easily simplified, keep the square roots in the answer, e.g. for instance, we can compare cost per encounter versus revenue by encounters, to find this information we have to total our cost by encounters and compare this to revenue by encounters. The University of Georgia; Writing Quadratic Equations; J. Wilson. The equation is y=4xsquare-4x+4. Great app almost always right, this helped me bring my grade up from a D+ to a A- In algebra. Gain more insight into the quadratic formula and how it is used in quadratic equations. There's nothing more frustrating than being stuck on a math problem. Find the Equation of a Quadratic (Parabola) Given 3 Points. Free quadratic functions calculator. Still a great one if you're struggling in math, but most of it is Perfect. Two questions: Say I have this quintic polynomial graph without the function. Two cloud shapes down and one to go. @Mel: It's explained on the line just before that, where it says: Those are the values we need to substitute. If you need help with your math homework, there are online calculators that can assist you. there's a similar question already on the site: As satisfying as the closed form might be, it is conceptually clearer to notice that in the case of 2 points $(x_1,y_1)$, $(x_2,y_2)$, to find the coefficients of a linear equation $y=ax+b$ that passes through those two points you plug the coordinates of those 2 points into that equation to get a system of two equations $$y_1 = a x_1 + b$$ $$y_2 = a x_2 + b$$ and then you solve that system of equations for $a,b$. When it comes to maths solving equations , dividing one number by another. And it's still a nice day! . Given two points on the graph of a linear function, we may find the slope of the line which is the function's graph, and then use the point-slope form to write. 2 02 Quadratic Equations. In the vertex form, the variables h and k are the coordinates of the parabola's vertex. If the discriminant is positive there are two solutions, if negative there is no solution, if equlas 0 there is 1 solution. Can you help me with the problem please. $$y_2=ax_2^2+bx_2+c$$ Not only []. We can set each expression equal to0and then solve for x: Comparing our example,x2+5x+6=0{x}^{2}+5x+6=0x2+5x+6=0, to the standard form of the quadratic equation (which can also just be called the quadratic), we get these values: Now we can use those in the quadratic formula and check, since we already know our answers are-2and-3: The ever-reliable quadratic formula confirms the values ofxas-2and-3. The equation of a a quadratic function can be determined from a graph showing the y-intecept, axis of symmetry and turn point. My website is in the very same niche as yours and my users would definitely benefit from some of the information you present here. Step 2: Pick a point on the graph Get Help with Homework; Track Way; Solve math equation; Clear . Homework is a necessary part of school that helps students review and practice what they have learned in class. Here's the appropriate section: https://www.intmath.com/forum/plane-analytic-geometry-37/. Substitute the first pair of values into the general form of the quadratic equation: f(x) = ax^2 + bx + c. Solve for a. We'll use that as our 3rd known point. Note: We could also make use of the fact that the x-value of the vertex of the parabola y = ax2 + bx + c is given by: Here's an example where there is no x-intercept. I have tried hard but found none. 6 3 Writing Two Step Equations Answers. I have no feedback here but really, This app works with me since 2015 when I saw the first ads on IG and im still using it until now, if you are a student you need to check this out, even my maths teacher can't explain as nicely, knows everything I need accept some graphing. To approximate a Sine curve with a quardric equation to generate a signal for a computer music system. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? What to do? And thanks for sharing "Meanies"! Substituting for x and y: 3 = a(-1 - 3)2 - 1 = 3 = a(-4)2 This operation is more complex, but is vital to scientists and mathematicians who need to formulate the equation that describes a chart of experimental values. Substitute the vertex's coordinates for h and k in the vertex form. For example, (1, 5), (2,11) and (3,19). Our goal is to make science relevant and fun for everyone. Solve for b. Also to see if you can use this to calculate sine values using two quadratic equations with one of them being the correction value add to the other to get it. In this video the tutor shows how to find the mirror point using a quadratic equation. The equation of the parabola is y = ax2 + bx + c, where a can never equal zero. f(x) = x2 6x + 8 Look at a in the equation. (b) Use the graph to find the roots of the equation x-2x-3=0. It may look a little scary, but youll get used to it quickly! But as in the previous case, we have an infinite number of parabolas passing through (1, 0). find the "=0" points; in between the "=0" points, are intervals that are either greater than zero (>0), or; What will be the vertex, focus and directrix of such parabola? That is, y = ax + bx + c y = ax + bx + c From these we obtain On parabola how can I find the equation of the axis of symmetry . I'm glad your found it useful! Can I use excel and choose polynomial and order 4? b is the slope of the tangent line at that point, and On the original blue curve, we can see that it passes through the point (0, 3) on the y-axis. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. Instead of x, you can also write x^2. Our goal is to make science relevant and fun for everyone. of the parabola on the graph, and plug it into the vertex form of a quadratic equation. For an example, let the vertex be (2, 3). First we need to identify the values for a, b, and c (the coefficients). I have some physical experiments done at various locations. Thank you so much for this page.. Vertex point: ( | ). This set of data is a given set of graph points that make up the shape of a parabola. Then use a different method to check your work. @billy: I added an extra line in there for you - hopefully it's clearer now. Look no further our experts are here to help. Direct link to Robert Lee's post if you mean find the solu, Posted 8 years ago. Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola The axis of symmetry is x = 0 so h also, We can use the vertex form to find a parabola's equation. The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b (b^2 - 4ac)) / (2a) Does any quadratic equation have two solutions? Get math help online by speaking to a tutor in a live chat. Since we know that b 0 = 1, the first equation becomes 2 = a. If the graph of y = f(x) = ax^2 + bx + c passes through (1,0) and (3,0) this means that f(1) = 0 and f(3) = 0. One such quadratic polynomial is f(x) = (x-1)(x-3, Use the given point (-1, 3), which says y is 3 for x equal to -1. Direct link to Karyn Williams's post I do not enjoy math and I, Posted 5 years ago. How to Find The Quadratic Equation From a Table/Points Top Tier Math 796 subscribers Subscribe 117 Share 8.2K views 1 year ago Algebra 1 So, those fun problems where you're given a table. We will graph using the properties. This is indeed the type of discussion and exercise that we need to see more of. Substitute the values of a, b and c into the general quadratic equation. Substituting a in the second equation yields 4 = 2b 2, which we simplify to b 2 = 2, or b = square root of 2, which equals approximately 1.41. Direct link to Nafia Farzana's post How do i know when the cu, Posted 5 years ago. Math is a subject that can be difficult for some students to grasp. y^2=-12x or Now the quadratic regression equation is as follows: y = ax2 + bx + c y = 8.05845x2 + 1.57855x- 0.09881 Which is our required answer. Solve mathematic question I can solve any mathematic question you give me. Then I just type the problem through calculator options from this app. There are multiple ways to reduce stress, including exercise, relaxation techniques, and healthy coping mechanisms. I would like to know how to find the equation of a quadratic function from its graph, including when it does not cut the x-axis. There is simply no way to make an analogous equation for any polynomial of degree y for y>4, not enough operations are defined by the rules of mathematics. Leave as is, rather than writing it as a decimal equivalent(3.16227766), for greater precision. He begins with saying that the Y-coordinate of . Thank you so much Murray Bourne. . How to find the equation of a quintic polynomial from its graph. Can the Spiritual Weapon spell be used as cover? What a cop-out. A quadratic equation has two solutions if the discriminant b^2 - 4ac is positive. Let's try another example using the following equation: Then we can check it with the quadratic formula, using these values: If you then plotted this quadratic function on a graphing calculator, your parabola would have a vertex of(1.25,10.125)with x-intercepts of-1and3.5. Be careful that the equation is arranged in the right form: Make sure you take the square root of the whole. In order to find a quadratic equation from a graph, there are two simple methods one can employ: using 2 points, or using 3 points. So long as a 0, you should be able to factor the quadratic equation. Calculate a quadratic function given the vertex point Computing a quadratic function out of three points. However, with a little practice and perseverance, anyone can learn to love math! Look up Lagrange polynomials. Explanation: Because the question specifies a function, we must discard the form that is not a function: x = ay2 +by + c and use only the form: y = ax2 +bx +c [1] I think this would a fast to . Quadratic equations have the general form: ax 2 + bx + c = 0 If the "a" coefficient is greater than 0, the parabola is "U-shaped" and if the "a" coefficient is less than 0, the parabola is "-shaped".