Question

Suppose a parabola has an axis of symmetry at x = -8 , a maximum height of 2, and passes through the point (-7, -1). Write the equation of the parabola in vertex form.

Answer 1

As it has a maximum value the coefficient of x^2 will be negative

The vertex will be at (-8,2)  so in vertex form it is

y = a(x + 8)^2 + 2
and as it passes through (-7,-1) we have:

-1  = a(-7+8)^2 + 2

-1 = a + 2  so a = -3

answer is  y = -3(x + 8)^2 + 2

in standard form this is y = -3x^2 -48x  - 190