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Chapter 6: Q21. (page 298)

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

-x2+4x=0

Short Answer

Expert verified

The solutions to the equation -x2+4x=0 are x=0,4.

Step by step solution

01

Step 1. Given Information.

Given to solve the equation -x2+4x=0 by graphing. And if the exact roots cannot be found, the consecutive integers between which the roots are located are to be determined.

02

Step 2. Explanation.

A quadratic equation has a real solution where the graph of the related function crosses or touches the x-axis.

Graphing the given equation using graphing calculator:

From the given graph, the function crosses the x axis at 0 and 4.

Hence the solutions to the equation -x2+4x=0are x=0,4.

03

Step 3. Conclusion.

Therefore, the solutions to the equation -x2+4x=0 are x=0,4

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Most popular questions from this chapter

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

f(x)=3x2

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=-4x2+5x

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)=-2x2+8x-3

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Write an algebraic expression for the kennel’s length.

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

f(x)=3-x2-6x
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