How do i find the function of this quadradic equation

Question

"The graph of a quadradic function passes through (-2, 0), (2, 0) and (0, 8).What is the function"

Please help me I cannot figure this out.

Answer 1

(-2,0), (2,0) and (0,8) have a quadratic equation through them

with x intercept s 2 and -2. that means the vertex has x coordinate midway = 0 and y coordinate = 8

it's an downward opening parabola with the y axis as the line of symmetry, or x=0

y = a(x-2)(x+2) = a(x^2 -4)

8 = a(-4)

a = 8/-4 = -2

the equation is

y = -2(x^2 -4)

or

y = -2x^2 +8 in vertex form

Answer 2

Two basic ways to do this;

1. Use y = ax²+bx+c . For (-2,0) when x = -2, y = 0. Similarly for the other two points. You will get 3 equations and 3 unknowns. The point (0,8) results in c-=8. So quickly you have two equations and two unknowns.
2. Use the fact that (-2,0) and (2,0) are x-intercepts, therefore 2 and -2 are roots and (x+2 and (x-2) are factors of the quadratic function. Now we have y = A(x+2)(x-2). Substitute x = 0 and y = 8 to solve for A.

Take if from there and check your work here:

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