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Chapter 9: Q17. (page 593)

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

鈭�x2+6x鈭�9=0

Short Answer

Expert verified

The root of the equation鈭�x2+6x鈭�9=0 is x=3.

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+6x−9=0 in the form fx=ax2+bx+c. 

Write the equation 鈭�x2+6x鈭�9=0 in standard form.

This equation is already in standard form.

Write the equation 鈭�x2+6x鈭�9=0in the form fx=ax2+bx+c.

fx=鈭�x2+6x鈭�9

03

Step 3. Plot the graph of the function fx=−x2+6x−9.

The graph of the functionfx=鈭�x2+6x鈭�9 is shown below.

04

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

Observe the graph of the function fx=x2鈭�3x鈭�4.

The graph intersects the x- axis exactly at one point x=3.

Therefore the root of the equation x2鈭�3x鈭�4=0 is x=3.

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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?

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

a2鈭�22a+121

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

An example of an exponential function is y=3x.

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.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

x2鈭�10x=鈭�15
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