Question

How do you make an equation for a parabola when you know the vertex (-1, -9), y intercept (0, -8), x intercepts (-4, 0) & (2, 0) with the axis of symmetry being x=-1

Answer 1

wow. first off all as we say these days tmi

Answer 2

because the zeros are at -4 and 2 you know it looks like
\[y=a(x+4)(x-2)\]

Answer 3

so find a, replace x by 0, set the result to -8 and solve

Answer 4

you get
\[y=-8=a(4)(-2)\]
\[-8=-8a\]
\[a=1\] so you have
\[y=(x+4)(x-2)\]

Answer 5

if you like you can multiply out and get
\[x^2+2x-8\]