How to find quadratic equation given vertex and a point

Asked by admin @ 10/11/2021 in Mathematics viewed by 320 People

What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.

vertex (0, 0), point (−2, 2)

Answered by admin @ 10/11/2021

1) The vertex equation of the quadratic function has the form:

y = A(x - h)² + k

Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

The coefficient A may be found when you have another point of the quadratic function.

2) Therefore, being the vertex (0,0), h = 0 and k = 0, and the equation is

y = Ax²

3) Replacing the coordinates of the point (-2,2) into the equation you get:

2 = A (-2)² ⇒ A = 2/4 = 1/2

4) The resulting equation is y = (1/2)x² ← answer

Since, the system is giving me an error, I had to put the second part of the answer in a separate file. Please, see the attached pdf file.

How to find quadratic equation given vertex and a point

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