Chapter 9: Q17. (page 593)

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$- x^{2} + 6 x - 9 = 0$

Short Answer

Expert verified

The root of the equation $- x^{2} + 6 x - 9 = 0$ is $x = 3$ .

Step by step solution

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

A quadratic function, which is written in the form, $f (x) = a x^{2} + b x + c$ , where, $a \neq 0$ is called the standard form of the quadratic function.

Step 2. Rewrite the equation −x2+6x−9=0 in the form fx=ax2+bx+c.

Write the equation $- x^{2} + 6 x - 9 = 0$ in standard form.

This equation is already in standard form.

Write the equation $- x^{2} + 6 x - 9 = 0$ in the form $f (x) = a x^{2} + b x + c$ .

$f (x) = - x^{2} + 6 x - 9$

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

The graph of the function $f (x) = - x^{2} + 6 x - 9$ is shown below.

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 $f (x) = x^{2} - 3 x - 4$ .

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

Therefore the root of the equation $x^{2} - 3 x - 4 = 0$ is $x = 3$ .

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Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$- x^{2} + 6 x - 9 = 0$

Short Answer

Step by step solution

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

Step 2. Rewrite the equation −x2+6x−9=0 in the form fx=ax2+bx+c.

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

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

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Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.−x2+6x−9=0

Short Answer

Step by step solution

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

Step 2. Rewrite the equation −x2+6x−9=0 in the form fx=ax2+bx+c.

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$- x^{2} + 6 x - 9 = 0$