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 31E

a.

To determine

To Express: The quadratic function in standard form.

Expert Solution

Answer to Problem 31E

the quadratic function is expressed in standard form as h(x)=1(x+12)2+54

Explanation of Solution

Given: The function is h(x)=(1xx2)

Calculation:

The quadratic function h(x)=(1xx2) 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)=(1xx2)h(x)=(x2x+1)h(x)=1(x2+x)+1                            [factor 1 the x terms]h(x)=1(x2+x+14)+1(114)     [complete the square: add 14 to the parentheses, subtract (114) outside]h(x)=1(x+12)2+54                          [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)=1(x+12)2+54

b.

To determine

To Sketch: The graph of the quadratic function.

Expert Solution

Explanation of Solution

Given: The function is h(x)=(1xx2)

Graph:

The standard form of the function is:

  h(x)=1(x+12)2+54

From the standard form it is observed that the graph is a parabola that opens upward and has vertex (12,54) . As an aid to sketching the graph, find the intercepts.

The y-intercept=h(0)=1 and the x-intercept is (12±52) and 0 . The graph g is sketched in the figure below.

Use graphing calculator to graph the function: h(x)=(1xx2)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 31E

c.

To determine

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

Expert Solution

Answer to Problem 31E

The value of maxima is h(12)=(54)

Explanation of Solution

Given: The function is h(x)=(1xx2)

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)=(54)

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