I wish I could show a picture this is for parabolas and quadratics

Question

So I have the given the points (-5,0) (-3,-1) and (9,0) I'm asked to use the given roots and point to find the equation as in f(x)=a(x-h)+k. There is no given vertex or a value so I'm not sure how to start this, I just need help remembering how to find vertex with the roots.

Answer 1

x intercepts are 9 and -5. There midpoint is (9-5)/2 = 4/2 = 2. the vertex has an x coordinate of 2

y=a(x-h)^2 + k

-1 =a(-3-2)^2 + k

-1 = 25a + k

0 = a(9-2)^2 + k

49a = -k

0 =a(-5-2) +k

k= -49a

-1 = 25a -49a = - 24a

a = 1/24

k=-49a =-49/24

y= (1/24)(x-2)^2 - 49/24

f(x) = (1/24)(x-2)^2 - 49/24