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Chapter 9: Q. 9.122 (page 958)

Graph fx=-2x2+12x-9by using transformations.

Short Answer

Expert verified

The graph of the given function is :

Step by step solution

01

Step 1. Given Information   

The given function isfx=-2x2+12x-9

02

Step 2. Separate the x  term from the constant.

First, separate the xterm from the constant and factor, we get:

fx=-2x2+12x-9fx=-2x2-6x-9

03

Step 3. Complete the square    

Now, Take half of 6and then square it, we get:

12路62=9

So, 9will complete the square.

04

Step 4.  Write in the required form 

The constant 9completes the square and then we have to subtract -2脳9=-18from the constant.

fx=-2x2-6x-9fx=-2x2-6x+9-9-(-18)f(x)=-2x-32+9

05

Step 5. Graph the function   

Looking at the h, k values, we see the graph will take the graph of y=x2and shift it to the right 3units and up 9 units and also multiply y-values in the parabola by -2. The parabola will be downwards because the leading coefficient is negative.

The graph of the given function is:

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