Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.3 - Analyzing Graphs of Functions - 2.3 Exercises - Page 194: 25


x = $\frac{1}{2}$

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 = $\sqrt {2x}$ - 1 Overall, we want to separate the x from all other constants. The first step would be to add 1 to each side. 0 + 1 = $\sqrt {2x}$ - 1 + 1 This gets: 1 = $\sqrt {2x}$ We then want to get rid of the square root. We can do this by squaring both sides. $1^{2}$ = $(\sqrt {2x})^{2}$ This gets: 1 = 2x We then want to divide both sides by 2 to get the x alone. $\frac{1}{2}$ = $\frac{2x}{2}$ This gets: $\frac{1}{2}$ = x Since x = $\frac{1}{2}$ when y = 0, x = $\frac{1}{2}$ is a zero of the function.
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