To Express: The quadratic function in standard form.

BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 29E

a.

To determine

Expert Solution

Answer to Problem 29E

the quadratic function is expressed in standard form as g(x)=3(x2)2+1

Explanation of Solution

Given: The function is g(x)=(3x212x+13)

Calculation:

The quadratic function g(x)=(3x212x+13) 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)=(3x212x+13)g(x)=3(x24x)+13                       [factor the x terms]g(x)=3(x24x+4)+13(34)     [complete the square: add 4 to the parentheses, subtract (34) outside]g(x)=3(x2)2+1                            [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)=3(x2)2+1

b.

To determine

Expert Solution

Explanation of Solution

Given: The function is g(x)=(3x212x+13)

Graph:

The standard form of the function is:

g(x)=3(x2)2+1

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

The y-intercept=g(0)=13 and There is no x-intercept . The graph g is sketched in the figure below.

Use graphing calculator to graph the function: g(x)=(3x212x+13)

c.

To determine

Expert Solution

Answer to Problem 29E

The value of minima is g(2)=(1)

Explanation of Solution

Given: The function is g(x)=(3x212x+13)

Calculation:

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

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