## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 2 - 2.3 - Analyzing Graphs of Functions - 2.3 Exercises - Page 194: 26

#### Answer

x= $\frac{-2}{3}$

#### Work Step by Step

Another word for zeros is the x-intercept. An x-intercept is where the line crosses the x-axis. For this to happen, the y-value must be 0, so to find the zeros of the function, the equation must equal 0. 0 = $\sqrt {3x + 2}$ Overall, we want to separate the x from all other constants. The first step would be to get rid of the square root. We can do this by squaring both sides. $0^{2}$ = $(\sqrt {3x + 2})^{2}$ This gets: 0 = 3x + 2 We then want to subtract 2 from both sides. 0 - 2 = 3x + 2 - 2 This gets: -2 = 3x We then want to divide both sides by 3 to get the x alone. $\frac{-2}{3}$ = $\frac{3x}{3}$ This gets: $\frac{-2}{3}$ = x Since x = $\frac{-2}{3}$ when y = 0, x = $\frac{-2}{3}$ is a zero of the function.

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