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Chapter 6: Q29. (page 298)

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

4x2-8x=5

Short Answer

Expert verified

The solutions to the equation 4x2-8x=5 lie between-1 and 0, 2 and 3.

Step by step solution

01

Step 1. Given Information.

Given to solve the equation 4x2-8x=5 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 between -1 and 0 and then in between 2 and 3.

Hence the solutions to the equation 4x2-8x=5 lie between -1 and 0, 2 and 3.

03

Step 3. Conclusion.

Therefore, the solutions to the equation 4x2-8x=5 lie between -1 and 0, 2 and 3.

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Most popular questions from this chapter

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)=3x2+10x

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

x2-3x=0

Use the related graph of each equation to determine its solutions.

2x2-5x-3=0

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)=12x2+3x+92
See all solutions

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