# To graph: the function f ( x ) = ( x − 3 ) 2 + 5 using the graph of a standard function and then applying transformations.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 37E
To determine

## To graph: the function f(x)=(x−3)2+5 using the graph of a standard function and then applying transformations.

Expert Solution

### Explanation of Solution

Given information:

the function is f(x)=(x3)2+5

Graph:

To plot the graph of f(x)=x2 ,use the plotting points method, substitute different value of x on f(x)=x2 to determine corresponding value of f(x) .

The table is thus obtained as:

 x -3 -2 -1 1 2 3 y 9 4 1 1 4 9

now plot each point of x along the horizontal axis and the corresponding value of f(x)=y along vertical axis and connect each point to form a smooth curve.

The graph of f(x)=x2 is obtained as:

Now, the graph of f(x)=(x3)2+5 is the graph of f(x)=x2 shifted 3 unitright , then 5 unit upwards.

The graphof f(x)=(x3)2+5 is obtained as:

Interpretation:

From the above graph it can be obtained that the graph of f(x)=(x3)2+5 is obtained by shifting the graph of f(x)=x2

3 unitright, then 5 unit upwards.

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