# To Express: The quadratic function in standard form.

### 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 9E

a.

To determine

Expert Solution

## Answer to Problem 9E

the quadratic function is expressed in standard form as f(x)=1(x3)29

### Explanation of Solution

Given: The function is f(x)=x26x

Calculation:

The quadratic function f(x)=x26x is expressed in standard form as:

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

The parabola opens upwards if a>0 .

Solve the function:

f(x)=(x26x)f(x)=1(x26x)                         [factor 1 from the x terms] f(x)=1(x26x+9)1.9           [complete the square : add 1 inside parentheses, subtract 19 outside]  f( x )=1 (x3) 2 9                       [factor and multiply]

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

Therefore, the quadratic function is expressed in standard form as f(x)=1(x3)29

b.

To determine

Expert Solution

## Answer to Problem 9E

the vertex is (h,k)=(3,9) .

x-intercept=0 and 6

y-intercept=f(0)=0

### Explanation of Solution

Given: The function is f(x)=x26x

Calculation:

The quadratic function f(x)=x26x is expressed in standard form as:

f(x)=1(x3)29

by completing the square. The graph of the function f is a parabola with vertex (h,k) , the vertex is (h,k)=(3,9) .

The y-intercept is given when x=0 , so y-intercept=f(0)=0

The x-intercept is given when y=0 , so x26x=0 which implies x(x6)=0

Therefore, x-intercept=0 and 6

c.

To determine

Expert Solution

### Explanation of Solution

Given: The function is f(x)=x26x

Graph:

The standard form of the function is:

f(x)=1(x3)29

From the standard form it is observed that the graph is a parabola that opens upward and has vertex (3,9) . As an aid to sketching the graph, find the intercepts. The y-intercept=f(0)=0 and the x-intercept=0 and 6 . The graph f is sketched in the figure below.

Use graphing calculator to graph the function: f(x)=x26x

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