# What is the vertex of y=3(x - 2)^2 + 5 ?

May 16, 2018

vertex: (2, 5)

#### Explanation:

$y = 3 {\left(x - 2\right)}^{2} + 5$

this is a parabola because of one variable squared and the other one is not so now write it in the standard form of parabolas which it is = to

## ______

Vertical :

${\left(x - h\right)}^{2} = 4 p \left(y - k\right)$

Horizontal:

${\left(y - k\right)}^{2} = 4 p {\left(x - h\right)}^{2}$

vertex = (h, k)

## ______

this $y = 3 {\left(x - 2\right)}^{2} + 5$ equation is vertical since $x$ is squared

subtract 5 from both sides:

$y - 5 = 3 {\left(x - 2\right)}^{2}$

divide both sides by 3:

$\left(y - 5\right) \frac{1}{3} = {\left(x - 2\right)}^{2}$

vertex:

$\left(2 , 5\right)$