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Chapter 9: Q16. (page 593)

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

x2鈭�3x鈭�4=0

Short Answer

Expert verified

The roots of the equationx2鈭�3x鈭�4=0 arex=鈭�1 and x=4.

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−4=0 in the form fx=ax2+bx+c. 

Write the equationx2鈭�3x鈭�4=0 in standard form.

This equation is already in standard form.

Write the equationx2鈭�3x鈭�4=0 in the form fx=ax2+bx+c.

fx=x2鈭�3x鈭�4

03

Step 3. Plot the graph of the function fx=x2−3x−4.

The graph of the functionfx=x2鈭�3x鈭�4 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 at the pointsx=鈭�1 and x=4.

Therefore, the roots of the equationx2鈭�3x鈭�4=0 arex=-1 and x=4.

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Most popular questions from this chapter

REASONING Provide a counterexample to the following statement. The vertex of a parabola is always the minimum of the graph.

Find the next three terms of each arithmetic sequence.

3,5,7,9,...

Use a table of values to graph the given equation. State the domain and range.

y=x2+3x+1

Solve each equation by completing the square. Round to the nearest tenth if necessary.

y2鈭�8y+16=36

Graph鈭�2,4,鈭�1,1,0,0,1,1,2,4. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function.
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