Question

How do you find the y coordinate of the vertex of a parabola?

Answer 1

See answer below

Explanation:

Given: a parabola equation

If the parabola equation is in the form: `f(x) = Ax^2 + Bx + C = 0`

The vertex is `(-B/(2A), f(-B/(2A)))`

Once you have the `x` value of the vertex, just evaluate the function with that `x`-value.

Example: `f(x) = 3x^2 -2x - 9`

`x = -(-2)/(2*3) = 2/6 = 1/3`

`f(1/3) = 3 (1/3)^2 - 2/1 * 1/3 - 9`

`f(1/3) = 3/1 * 1/9 - 2/3 - 9`

`f(1/3) = 3/9 - 2/3 - 9`

`f(1/3) = 1/3 - 2/3 - 9/1 * 3/3`

`f(1/3) = -1/3 - 27/3 = -28/3 = -9 1/3`

vertex: `(1/3, -28/3)`