Question

write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)

Answer 1

y =
`-(19)/(9) (x+3)^(2) + 5`

Explanation:

The form of a quadratic function is y = a(x-h)^2 + k, where (h, k) is the vertex. From the givens in the problem, we know that (h, k) = (-3, 5), and another point on it will be (x, y) = (0, -14). Plug both of these into the equation to get:

-14 = a(3)^2 + 5

-19 = 9a

a = -19/9

∴ The equation is y =
`-(19)/(9) (x+3)^(2) + 5`