Question

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

Answer 1

`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]}