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

Answer 1

y=a(x-h)²+k

(h,k) = (-3,5)

y=a(x- -3)²+5

at (0,-14)

-14=a(0+3)²+5

a=-19/9

y=(-19/9)(x+3)²+5

Answer 2

Quadratic functional equation in vertex form is:

y = a(x – h)² + k

where the vertex is at (h,k), so using the vertex given gives:

y = a(x – (-3))² + 5

y = a(x + 3)² + 5

Then substituting the point given as part of the function:

-14 = a(0 + 3)² + 5

-14 = 9a + 5

-19 = 9a

A = -19/9

Therefore the equation is:

y = -(19/9)(x + 3)² + 5