quadratic functions

Question

Determine the quadratic function,  f(x)=ax^2+bx+c, whose vertex is (3, 7) and passes through the point (5, -9). Please show all of your work.

Answer 1

Parabola form is y = ax^2+bx+c

Vertex form is y = a(x-h)^2+k -----> (1)

Given (x,y) = (5,-9)

Vertex (h,k) = (3,7)

Now find a

-9 = a(5-3)^2+7

-9 = 4a+7

-9-7 = 4a

a = -16/4

a = -4

Substitute a value and vertex in (1).

y = -4(x-3)^2+7

y = -4(x^2+9-6x)+7

y = -4x^2-36+24x+7

y = -4x^2+24x-29

This is in quadratic form.