What are the x-intercepts for this equation? f (x) = (x – 6) (x + 1) %3D

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question:**

What are the x-intercepts for this equation?

**Equation:**

\[ f(x) = (x - 6)(x + 1) \]

**Explanation:**

The x-intercepts of a function are the values of \(x\) where the function \(f(x)\) equals zero. To find the x-intercepts of the given equation, we need to solve the equation for \(x\) when \(f(x) = 0\).

\[ (x - 6)(x + 1) = 0 \]

Setting each factor equal to zero gives:

1. \(x - 6 = 0 \)  ⇒  \( x = 6 \)
2. \(x + 1 = 0 \)  ⇒  \( x = -1 \)

Therefore, the x-intercepts are \( x = 6 \) and \( x = -1 \).
Transcribed Image Text:**Question:** What are the x-intercepts for this equation? **Equation:** \[ f(x) = (x - 6)(x + 1) \] **Explanation:** The x-intercepts of a function are the values of \(x\) where the function \(f(x)\) equals zero. To find the x-intercepts of the given equation, we need to solve the equation for \(x\) when \(f(x) = 0\). \[ (x - 6)(x + 1) = 0 \] Setting each factor equal to zero gives: 1. \(x - 6 = 0 \) ⇒ \( x = 6 \) 2. \(x + 1 = 0 \) ⇒ \( x = -1 \) Therefore, the x-intercepts are \( x = 6 \) and \( x = -1 \).
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