# 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 23E

a.

To determine

Expert Solution

## Answer to Problem 23E

the quadratic function is expressed in standard form as  f(x)=1(x+1)22

### Explanation of Solution

Given: The function is f(x)=(x2+2x1)

Calculation:

The quadratic function f(x)=(x2+2x1) 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)=(x2+2x1) f(x)=1(x2+2x)1                        [factor 1 the x terms] f(x)=1(x2+2x+1)1(11)       [complete the square: add 1 to parentheses, subtract (11) outside] f(x)=1(x+1)22                          [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(x+1)22

b.

To determine

Expert Solution

### Explanation of Solution

Given: The function is f(x)=(x2+2x1)

Graph:

The standard form of the function is:

f(x)=1(x+1)22

From the standard form it is observed that the graph is a parabola that opens upward and has vertex (1,2) . As an aid to sketching the graph, find the intercepts.

The y-intercept=f(0)=1 and The x-intercept is 2 . The graph f is sketched in the figure below.

Use graphing calculator to graph the function: f(x)=(x2+2x1)

c.

To determine

Expert Solution

## Answer to Problem 23E

The value of minima is f(1)=2

### Explanation of Solution

Given: The function is f(x)=(x2+2x1)

Calculation:

From the above graph it is seen that the parabola opens upward, since the coefficient of x2 is positive, fhas minimum value. The value of minima is f(1)=2

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