Question

ALGEBRA 2
MEDAL!!!
12. Suppose a parabola has an axis of symmetry at x=-7, a maximum height of 4 and also passes throughout the point (-6,0). Write the equation of the parabola in vertex form.

Answer 1

i need step by step please

Answer 2

the axis of symmetry is -7
and the max height is four

the vertex is (-7, 4) and the parabola opens downward

vertex form
y = a(x - h)^2 + k [the "a" will be negative because the parabola opens downward]

vertex is
(h, k)

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

solve for "a" by subbing in the given point (-6, 0)

0 = -a(-6 + 7)^2 + 4
0 = -a * 1 + 4
0 = -a + 4
-4 = -a
4 = a

so your equation is
y = -4(x + 7)^2 + 4