Answer to Question #169165 in Algebra for william

Question

What is the vertex given the equation: y=2/3 square root of x+4-2

Vertex:

Answer 1

our function is

$y=\tfrac{2}{3}\sqrt{\smash[b]{x+4}}-2$

Standard form of the square root function is

$y=a\sqrt{\smash[b]{b(x-h)}}+k$ , where

$b=±1$ and

$h, k$ - vertex

Convert our function

$y=\tfrac{2}{3}\sqrt{\smash[b]{x+4}}-2=\tfrac{2}{3}\sqrt{\smash[b]{-(-x-4)}}-2$

Therefore vertex is $(-4, -2)$

Also we can see vertex on the graph of the function.