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Chapter 6: Q33. (page 291)

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=-x2-9

Short Answer

Expert verified

The function has maximum value that is -9.

Step by step solution

01

Step 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a鈮�0,the x-coordinate of vertex is -b2a.

The graph off(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
02

Step 2. Given Information.

The given function is f(x)=-x2-9

03

Step 3. Solution.

In the function f(x)=-x2-9, we have

a=-1,b=0,c=-9

Here, a=-1<0

So, the graph opens down and has a maximum value.

The maximum value of the function is the y-coordinate of the vertex.

Thex-coordinate of the vertex is

鈭�b2a=鈭�02(鈭�1)..........a=鈭�1,b=0=0

Find they-coordinate of the vertex by evaluating the function for x=0.

f(0)=-02-9=-9

So, the maximum value of function is -9.

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Most popular questions from this chapter

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

-12x+x2=-36

The graph of which of the following equations is symmetrical about the y-axis?

  1. y=x2+3x-1
  2. y=-x2+x
  3. y=6x2+9
  4. y=3x2-3x+1

Give an example of a quadratic function and state its related quadratic equation.

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-9x+9

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=3x2
See all solutions

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