Question

Find a function f whose graph is a parabola with the given vertex and that passes through the given point.

vertex (−1, 8) point (−2, −1)
f(x) =?

Answer 1

y=-9(x+1)^2+8

start with the vertex form of a parabola:

y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.

1. plug in the vertex coordinates

y=a(x+1)^2+8

2. to find "a", plug in the point coordinates in the function from step 1 for x and y

-1=a(-2+1)^2+8

when you solve this equation, you will find that a=-9

3. substitute "a" value in the equation from step 1

Done

Answer 2

y=-7(x+1)^2 +8

Explanation:

Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.