Question

Find the equation of the quadratic function g whose graph is shown below.

(5,3)
(6.0)
8
201 12 114
g(x) = 0

Answer 1

y = -3(x - 5)^2 + 3

Explanation:

Because we're given the maximum/vertex of the quadratic function and at least one of the roots, we can find the equation of the quadratic equation using the vertex form which is

`y = a(x-h)^2+k`, where a is a constant (determine whether parabola will have maximum or minimum), (h, k) is the vertex (a maximum for this problem), and (x, y) are any point on the parabola:

Since our maximum/vertex is (5, 3), and one of our roots is (6, 0), we can plug everything in and solve for a:

`0=a(6-5)^2+3\\0=a(1)^2+3\\0=a+3\\-3=a`

Thus, the general equation (without distribution) is y = -3(x - 5)^2 + 3