# What is the vertex of the parabola y=3(x-4)^2-22?

May 10, 2016

$\left(4 , - 22\right)$

#### Explanation:

The equation:

$y = 3 {\left(x - 4\right)}^{2} - 22$

is in vertex form:

$y = a \left(x - h\right) + k$

with multiplier $a = 3$ and vertex $\left(h , k\right) = \left(4 , - 22\right)$

The nice thing about vertex form is that you can immediately read the vertex coordinates from it.

Notice that ${\left(x - 4\right)}^{2} \ge 0$, taking its minimum value $0$ when $x = 4$. When $x = 4$ we have $y = 3 {\left(4 - 4\right)}^{2} - 22 = 0 - 22 = - 22$.

So the vertex is at $\left(4 , - 22\right)$.