Quadratic Function Form - Vertex

Question

A parabola opening up or down has vertex (0, 1) and passes through (8, –9). Write its equation in vertex form.

Simplify any fractions

Answer 1

y=ax^2 +1

-9 = 64a +1

a = -10/64 =-5/32

y = -(5/32)x^2 +1 is the downward opening parabola with vertex = (0,1) through (8,-9)

in more express vertex form, add in the zero

y =-(5/32)(x-0)^2 +1

vertex form is y=a(x-h)^2 +k where (h,k) = the vertex

if opening horizontally, left or right were an option

then

x= a(y-1)^2 + 0

8 = a(-9-1)^2

a = 8/100 = 2/25

x = (2/25)(y-1)^2 is the rightward opening parabola with given vertex through (8,-9)

also an infinite number of slanted parabolas with that same vertex through (8,-9)