Find the quadratic function that has the given vertex and go

Find the quadratic function that has the given vertex and goes through the given point

Vertex: (-4,-4) Point: (-5,8)

f(x)=___________

vertex = ( -4 , -4 )

point ( -5 , 8 )

standard quadratic equation in vertex form is given by

y = a ( x-h)^2 + k

pluging the values in the equation

8 = a ( -5 + 4 )^2 - 4

solving the equation for a

8 + 4 = a

a = 12

therefore, equation becomes

y = 12 ( x + 4)^2 - 4

y = 12 (x^2 + 8x + 16 ) - 4

y = 12x^2 +96x +192 - 4

f(x) = 12x^2 + 96x + 188