# 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 30E

a.

To determine

## To Express: The quadratic function in standard form.

Expert Solution

the quadratic function is expressed in standard form as g(x)=2(x+2)2+3

### Explanation of Solution

Given: The function is g(x)=(2x2+8x+11)

Calculation:

The quadratic function g(x)=(2x2+8x+11) 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:

g(x)=(2x2+8x+11)g(x)=2(x2+4x)+11                       [factor the x terms]g(x)=2(x2+4x+4)+11(24)     [complete the square: add 4 to the parentheses, subtract (24) outside]g(x)=2(x+2)2+3                           [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 g(x)=2(x+2)2+3

b.

To determine

Expert Solution

### Explanation of Solution

Given: The function is g(x)=(2x2+8x+11)

Graph:

The standard form of the function is:

g(x)=2(x+2)2+3

From the standard form it is observed that the graph is a parabola that opens upward and has vertex (2,3) . As an aid to sketching the graph, find the intercepts.

The y-intercept=g(0)=11 and There is no x-intercept . The graph f is sketched in the figure below.

Use graphing calculator to graph the function: g(x)=(2x2+8x+11)

c.

To determine

### To Find: The maximum or minimum value of the function.

Expert Solution

The value of minima is g(2)=(3)

### Explanation of Solution

Given: The function is g(x)=(2x2+8x+11)

Calculation:

From the above graph it is seen that the parabola opens upward, since the coefficient of x2 is positive, f has minimum value. The value of minima is g(2)=(3)

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