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Chapter 6: Q32. (page 298)

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

x2+3x-2=0

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information.

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

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

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=-0.25x2-3x

Write an expression for the minimum value of a function of the form y=ax2+c, where a>0. Explain your reasoning. Then use this function to find the minimum value of y=8.6x2-12.5

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)=x2-9

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=0.5x2-1

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

fx=-6x2+9x
See all solutions

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