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Chapter 9: Q12. (page 566)

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

x2=12

Short Answer

Expert verified

The roots of the equation x2=12are role="math" localid="1647756035663" x=鈭�3.5and x=3.5.

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=12 in the form fx=ax2+bx+c.

Write the equation x2=12in standard form.

The standard form of this equation is

x2鈭�12=0

Write the equation x2鈭�12=0in the form fx=ax2+bx+c.

fx=x2鈭�12

03

Step 3. Plot the graph of the function fx=x2−12.

The graph of the function fx=x2鈭�12is shown below.

04

Step 4. Solve the equation x2=12 from the graph of the function fx=x2−12.

Observe the graph of the function fx=x2鈭�12.

The graph intersects the x- axis at the points near about x=鈭�3.5and x=3.5.

Therefore the roots of the equation x2鈭�12=0arex=鈭�3.5 and x=3.5.

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Most popular questions from this chapter

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

a2+12a+36

Consider y=x2鈭�5x+4

Graph the function.

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

x2鈭�12x+32

Considery=x2鈭�5x+4

Write the equation of the axis of symmetry.

Write the equation for the nth term of each geometric sequence.

鈭�1,1,鈭�1,1,.....
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