Question

Write the equation for the graphed function. I worked out y = 5 - 4 (x + 4)^2 but that isn't right. Any help would be appreciated.

Answer 1

Vertex form for a parabola with vertex (p,q) is

$y = a(x-p)^2 + q$

We have (p,q)=(-4,5) and another point (-3,2) so we can solve for a:

$2 = a(-3 - -4)^2 + 5$

$2 = a + 5$

$a = -3$

Putting it together,

Answer: $y = -3(x + 4)^2 + 5$

We could multiply that out if we like but I won't bother.