How do you write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)?

1 Answer
Apr 24, 2018

y= -19/9(x+3)^2+5

Explanation:

If an equation representing a parabola is in vertex form such as

y=a(x-k)^2+h

then its vertex will be at (k, h). Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form

y=a(x+3)^2+5

If this parabola also passes through the point (0, -14) then we can determine the a parameter.

-14=a(0+3)^2+5

9a=-19

a=-19/9

So our equation in vertex form is

y= -19/9(x+3)^2+5

graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}