what is the quadratic function equation who's vertex is (-5,9) and passes through the point (-7,-15)

Answer 1

Very easy if you use the vertex form:

y = a(x-h)² + k

where a is a constant to be determined and (h,k) = (-5,9) is the location of the vertex.

y = a(x-(-5))² + 9

y = a(x+5)² + 9

To find the value of the constant a, plug in the other given point, (-7,-15):

-15 = a(-7+5)² + 9

Solve for a.