Question

find the equations of the quadratics given the following information
zeros of 5 and 9
an optimal value of -2
using the formula y=a(x-s)(x-t)

Answer 1

we can start with
y = a(x-5)(x-9)

the vertex , where the function has an optimal value of -2, must be midway between the zeros , that is,
when the x = 7
so (7,-2) is the vertex, let's sub that into our equation
-2 = a((7-5)(7-9)
-2 = a(-4)
a = 1/2

equation: y = (1/2)(x-5)(x-9)