# Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 40

$f(x)=-(x+2)^2-9$

#### Work Step by Step

Since the shape of the graph is a $f(x) = x^2$ we will start with that function: $f(x)=x^2$ The first transformation is 2 units left. Remember that shifts to the left or right are done inside of the function and that left or right transformations have an opposite sign so that left shifts are positive and right shifts are negative. $f(x)=(x+2)^2$ The second transformation is nine units up. Shifts up and down are added to the end of the function. $f(x)=(x+2)^2+9$ Last is the reflection over the x-axis. This is done by multiplying the right side by -1 $f(x)=-(x+2)^2-9$

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