# 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 32E

a.

To determine

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

Expert Solution

the quadratic function is expressed in standard form as h(x)=4(x+12)2+4

### Explanation of Solution

Given: The function is h(x)=(34x4x2)

Calculation:

The quadratic function h(x)=(34x4x2) 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 downwards if a<0 .

Solve the function:

h(x)=(34x4x2)h(x)=(4x24x+3)h(x)=4(x2+x)+3                            [factor 4 the x terms]h(x)=4(x2+x+14)+3(414)    [complete the square: add 14 to the parentheses, subtract (414) outside]h(x)=4(x+12)2+4                          [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 h(x)=4(x+12)2+4

b.

To determine

Expert Solution

### Explanation of Solution

Given: The function is h(x)=(34x4x2)

Graph:

The standard form of the function is:

h(x)=4(x+12)2+4

From the standard form it is observed that the graph is a parabola that opens upward and has vertex (12,4) . As an aid to sketching the graph, find the intercepts.

The y-intercept=h(0)=3 and the x-intercept is 32,12 and 0 . The graph g is sketched in the figure below.

Use graphing calculator to graph the function: h(x)=(34x4x2)

c.

To determine

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

Expert Solution

The value of maxima is h(12)=(4)

### Explanation of Solution

Given: The function is h(x)=(34x4x2)

Calculation:

From the above graph it is seen that the parabola opens downward, since the coefficient of x2 is negative, g has maximum value. The value of maxima is h(12)=(4)

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