Find the quadratic function whose vertex is (4,3) and y-intercept is −9.

What we know:
Find the quadratic function whose vertex is (4,3) and y-intercept is −9.

Start with vertex form:
f (x)=a (x-h)²+ k when vertex is (4,3) h=4,k=3, point (0,-9)
f (x)= a (x-4)²+3 sub in (4,3)
(-9)=a (0-4)²+3 sub in (0,-9)
-9=16a+3 simplify, now solve for a
-9-3=16a+3-3 subtraction property
-12=16a
-12/16=16/16a division property
-3/4=a

rewrite vertex form using vertex (4,3), a=-3/4

Quadratic equation: f (x)=-3/4 (x-4)²+3