It means we have three equations, one for each of the points — since we know the points given must satisfy the unknown equation. We'll assume the axis of the given parabola is vertical. Well, if we restrict ourselves to parabolas given by quadratic equations, that is curves which the formthen since there are three unknown quantities, we can expect that we can fit such a curve to three distinct points.
System of Equations method To find the unique quadratic function for our blue parabola, we need to use 3 points on the curve.
Find the equation of a quadratic function with vertex 0,0 and containing the point 4,8. Solve for "a. Remember y and f x represent the same quantity. Take the two resulting equations and solve the system you may use any method.
Fortunately the ancient Chinese were able to develop a general technique for solving such systems of equations. Plug in the coordinates for x and y into the general form.
He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. Use the following steps to write the equation of the quadratic function that contains the vertex 0,0 and the point 2,4.
Here are some of them in green : And don't forget the parabolas in the "legs down" orientation: So how do we find the correct quadratic function for our original question the one in blue?