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Factor to find all x-intercepts of the function. 2 f(x) = x² - 2x + 1 −

Factor to find all x-intercepts of the function. 2 f(x) = x² - 2x + 1 −

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Instruction:** Factor to find all x-intercepts of the function. **Function:** \[ f(x) = x^2 - 2x + 1 \] **Explanation:** To find the x-intercepts of the function given by \( f(x) = x^2 - 2x + 1 \), factor the quadratic equation. Look for two numbers that multiply to +1 (the constant term) and add to -2 (the coefficient of x). The factored form is: \[ f(x) = (x - 1)(x - 1) \] Setting it to zero gives: \[ (x - 1)^2 = 0 \] Thus, the x-intercept is at: \[ x = 1 \]
Transcribed Image Text:**Instruction:** Factor to find all x-intercepts of the function. **Function:** \[ f(x) = x^2 - 2x + 1 \] **Explanation:** To find the x-intercepts of the function given by \( f(x) = x^2 - 2x + 1 \), factor the quadratic equation. Look for two numbers that multiply to +1 (the constant term) and add to -2 (the coefficient of x). The factored form is: \[ f(x) = (x - 1)(x - 1) \] Setting it to zero gives: \[ (x - 1)^2 = 0 \] Thus, the x-intercept is at: \[ x = 1 \]
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