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Chapter 9: Q11. (page 566)

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

鈭�x2+3x鈭�1=0

Short Answer

Expert verified

The roots of the equation鈭�x2+3x鈭�1=0 are x=0.4andx=2.6.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, fx=ax2+bx+c, where,a鈮�0 is called the standard form of the quadratic function.

02

Step 2. Rewrite the equation −x2+3x−1=0 in the form fx=ax2+bx+c.

Write the equation 鈭�x2+3x鈭�1=0in standard form.

This equation is already in standard form.

Write the equation 鈭�x2+3x鈭�1=0in the form fx=ax2+bx+c.

fx=鈭�x2+3x鈭�1fx=鈭�x2+3x鈭�1

03

Step 3. Plot the graph of the function fx=−x2+3x−1.

The graph of the function fx=鈭�x2+3x鈭�1 is shown below.

04

Step 4. Solve the equation −x2+3x−1=0 from the graph of the function fx=−x2+3x−1.

Observe the graph of the function fx=鈭�x2+3x鈭�1.

The graph intersects the x- axis at the points near about x=0.4and x=2.6.

Therefore the roots of the equation 鈭�x2+3x鈭�1=0are x=0.4and x=2.6.

.

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Most popular questions from this chapter

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Use the graph of the quadratic equation shown below to answer each question.

A What is the vertex?

B What is they-intercept?

C What is the axis of symmetry?

D What are the roots of the corresponding quadratic equation?

What is the vertex of the parabola graphed below?

A2,0B0,2C鈭�2,2D2,鈭�2

Describe how the graph of the given function is related to the graph of

fx=x2hx=2x2

REASONING The graph of a quadratic function has a vertex at 2,0. One point on the graph is 5,9. Find another point on the graph. Explain how you find it.

Graph each function. Find the y-intercept, and state the domain and range.

y=鈭�311x
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