Solve the following quadratic function to find the x-intercepts: f(x) = x² - 6x +9 x=3 x = -3 and 3 Ox= 9 and -6 O x = -5 and -1

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Solving for X-Intercepts of a Quadratic Function**

Given the quadratic function:
\[ f(x) = x^2 - 6x + 9 \]

**Objective:** Find the x-intercepts.

**Options:**
- \( x = 3 \)
- \( x = -3 \) and \( 3 \)
- \( x = 9 \) and \( -6 \)
- \( x = -5 \) and \( -1 \)

**Solution Approach:**

To find the x-intercepts, set the function equal to zero:
\[ x^2 - 6x + 9 = 0 \]

This can be factored as:
\[ (x - 3)^2 = 0 \]

Thus, the x-intercept is:
\[ x = 3 \] 

Verify by substituting back into the original equation. The correct answer is \( x = 3 \).
Transcribed Image Text:**Solving for X-Intercepts of a Quadratic Function** Given the quadratic function: \[ f(x) = x^2 - 6x + 9 \] **Objective:** Find the x-intercepts. **Options:** - \( x = 3 \) - \( x = -3 \) and \( 3 \) - \( x = 9 \) and \( -6 \) - \( x = -5 \) and \( -1 \) **Solution Approach:** To find the x-intercepts, set the function equal to zero: \[ x^2 - 6x + 9 = 0 \] This can be factored as: \[ (x - 3)^2 = 0 \] Thus, the x-intercept is: \[ x = 3 \] Verify by substituting back into the original equation. The correct answer is \( x = 3 \).
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