# The coordinates of the vertex of a quadratic function f.

### 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 3.1, Problem 5E

a.

To determine

## To Find: The coordinates of the vertex of a quadratic function f.

Expert Solution

The coordinates of the vertex are (3,4)

### Explanation of Solution

Given: The function is f(x)=x2+6x5

Calculation:

The quadratic function f(x)=x2+6x5 is expressed in standard form as:

f(x)=a(xh)2+k , by completing the square. The graph of f is a parabola with vertex (h,k) ,

The parabola opens downward if a<0 .

Solve the function:

f(x)=x2+6x5        =1(x26x)5                      [factor 1 from the x terms]        =1(x26x+9)5(1)9    [complete the square : add +9 inside parentheses, subtract (1)9 outside]         =1 (x3) 2 +4                        [factor and multiply]

On comparing the above equation with standard form f(x)=a(xh)2+k ,

Therefore, the coordinates of the vertex are (h,k)=(3,4)

b.

To determine

### To Find: The maximum or minimum value of f.

Expert Solution

the coefficient of x2 is negative, f has a maximum value. The maximum value is f(3)=4

### Explanation of Solution

Given:The function is f(x)=x2+6x5

Calculation:The standard form of the function is:

f(x)=1(x3)2+4

If a<0 , then the maximum value of f is f(h)=k , and is represented as f(3)=4

Since, the coefficient of x2 is negative, f has a maximum value. The maximum value is f(3)=4

c.

To determine

### To Find: The domain and range of f.

Expert Solution

the domain is from (,) and the range is (,4]

### Explanation of Solution

Given: The function is f(x)=x2+6x5

Calculation:

The standard form of the function is:

f(x)=1(x3)2+4

It is observed from the standard form of the function thatthe domain is from (,) and the range is (,4]

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!