math pre calculus

Question

Write the equation of the parabola if: the vertex is (-2, -8), ad the point (-20, 12) is on the parabola

Answer 1

It's either an upward opening or leftward opening parabola

for upward: y=a(x+2)^2 -8, solve for a by pluggint in x=-20, y= 12

12=a(-20+2)^2 - 8

20=324a

a = 20/324= 5/81

y=(5/81)(x+2)^2 -8

for leftward: x =a(y+8)^2 -2

-20=a(12+8)^2-2

-18 =400a

a = -18/200= -9/100

x = (-9/100)(y+8)^2 -2

But if you're focused on "the parabola" as if there is only one answer, go with the upward opening parabola, it's more standard. Truth is there are an infinite number of parabolas going through the given point with the given vertex, all at different angles. between the upward and leftward ones.Half upward, half leftward, and every angle inbetween.