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

Jul 7, 2018

See answer below

#### Explanation:

Given: a parabola equation

If the parabola equation is in the form: $f \left(x\right) = A {x}^{2} + B x + C = 0$

The vertex is $\left(- \frac{B}{2 A} , f \left(- \frac{B}{2 A}\right)\right)$

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

Example: $f \left(x\right) = 3 {x}^{2} - 2 x - 9$

$x = - \frac{- 2}{2 \cdot 3} = \frac{2}{6} = \frac{1}{3}$

$f \left(\frac{1}{3}\right) = 3 {\left(\frac{1}{3}\right)}^{2} - \frac{2}{1} \cdot \frac{1}{3} - 9$

$f \left(\frac{1}{3}\right) = \frac{3}{1} \cdot \frac{1}{9} - \frac{2}{3} - 9$

$f \left(\frac{1}{3}\right) = \frac{3}{9} - \frac{2}{3} - 9$

$f \left(\frac{1}{3}\right) = \frac{1}{3} - \frac{2}{3} - \frac{9}{1} \cdot \frac{3}{3}$

$f \left(\frac{1}{3}\right) = - \frac{1}{3} - \frac{27}{3} = - \frac{28}{3} = - 9 \frac{1}{3}$

vertex: $\left(\frac{1}{3} , - \frac{28}{3}\right)$