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Chapter 6: Q43. (page 291)

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

f(x)=34x2-5x-2

Short Answer

Expert verified

The function has minimum value that is -10.333.

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 of f(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)=34x2-5x-2

03

Step 3. Solution.

In the function f(x)=34x2-5x-2, we have a=34,b=-5,c=-2

Here, a=34>0

So, the graph opens up and has a minimum value.

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

Thex-coordinate of the vertex is

鈭�b2a=鈭�鈭�52(34)..........a=34,b=鈭�5=3.333

Find they-coordinate of the vertex by evaluating the function for x=3.333.

f(3.333)=343.3332-53.333-2=-10.333

So, the minimum value of function is -10.333.

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Most popular questions from this chapter

State whether the graph of each quadratic function opens up or down. Then state whether the function has a maximum or minimum value.

a.f(x)=3x2+4x鈭�5b.f(x)=鈭�2x2+9c.f(x)=鈭�5x2鈭�8x+2d.f(x)=6x2鈭�5x

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

f(x)=3x2

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+12x+36

Use the related graph of each equation to determine its solutions x2+3x-4=0.

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

x2+4x-4=0
See all solutions

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