Answer:
[tex]y = \frac{1}{4} (x-0)^{2} -4[/tex]
Step-by-step explanation:
Vertex formula is y = a(x-h)^{2} +k
You know that the vertex is (0,-4)
and the point is passes through is (-8, 12)
All you need to do is substitute the points into the formula
1. For your vertex Coordinate (h,k) is the same as (x,y) but (h,k) represents the coordinates of the vertex.
[tex]y = a(x-0)^{2} -4)[/tex]
This is the formula with the vertex points substituted in
2. Next, substitute the pass through coordinate point (-8, 12) into the vertex formula we did in step 1.
[tex]12 = a(-8 -0)^{2} -4[/tex]
[tex]12 = a(-8)^{2} -4[/tex] (square -8)
[tex]12 = 64a -4[/tex] (multiple a and 64)
[tex]16 = 64a[/tex] (add 4 to both sides)
[tex]\frac{16 = 64a}{64}[/tex] (divide by 64 to get a by itself)
[tex]a = \frac{1}{4}[/tex] (this is the value for a)
3. Combine your answers into the vertex formula:
[tex]y = \frac{1}{4} (x-0)^{2} -4[/tex]
