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Chapter 2: Q. 80 (page 114)

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

f(x)=3x2+6x+1

Short Answer

Expert verified

The graph of the given equation is

Step by step solution

01

Step 1. Given information

Given expression:

f(x)=3x2+6x+1

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's add and subtract 1 inside the bracket, therefore

f(x)=3x2+6x+1=3(x2+2x)+1=3(x2+2x+1-1)+1=3(x+1)2-3+1=3(x+1)2-2

04

Step 4. Graphing using shifting technique

In order to graph the given expression, we need to draw the graph of f(x)=x2i.e.

05

Step 5. Graphing the actual expression

Replace xby x+1in the expression

f(x)=x2=(x+1)2

Now multiply it with 3and subtracting 2we get,

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