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Chapter 2: Q. 82 (page 114)

complete the square of each quadratic expression. Then graph each function using the technique of shifting.

f(x)=-2x2-12x-13

Short Answer

Expert verified

The graph of the given equation is

Step by step solution

01

Step 1. Given information

Given expression:

f(x)=-2x2-12x-13

02

Step 2. Write the concept

In order to complete the square, we will add or subtract some numbers in order to simplify it.

03

Step 3. Calculation

Let us take out -2from the given expression therefore,

-2x2-12x-13=-2x2+6x+132Nowwesubtract9fromitf(x)=-2x2+6x+9+132-9=-2(x+3)2+132-9=-2(x+3)2-52

04

Step 4. Graphing using shifting technique

In order to graph the given expression we need to draw the graph of x2i.e.

05

Step 5. Graphing the actual expression

Replace y=f(x)withy=f(x-h)here h=3 therefore,

06

Step 6. Shifting vertically

The function y=f(x)-kwillbeshiftedverticallydownwardbykunitsf(x)=(x+3)2by52units.

Now, the the actual graph will be the reflection of above graph multiplied by 2.

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Exploration Graph y=x. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?

True or False If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers.

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x
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