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What is the $x$ -intercept of the graph of $y=(x-5)^{2}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-25$ $\newline$ (B) $-5$ $\newline$ (C) $5$ $\newline$ (D) $25$

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Transformations of functions

Full solution

Q. What is the

x

-intercept of the graph of

y=(x-5)^{2}

?

\newline

Choose

1

answer:

\newline

(A)

-25

\newline

(B)

-5

\newline

(C)

5

\newline

(D)

25

Set $y$ equal to $0$ : To find the x-intercept of the graph, we need to set $y$ equal to $0$ and solve for $x$ . So, we set the equation $y = (x - 5)^2$ to $0$ : $0 = (x - 5)^2$
Find x value: Now, we need to find the value of $x$ that makes the equation true. Since we have a square, we can take the square root of both sides to solve for $x$ . $\sqrt{0} = \sqrt{(x - 5)^2}$
Take square root: Taking the square root of both sides gives us: $\newline$ $0 = x - 5$
Isolate x: To isolate x, we add $5$ to both sides of the equation: $\newline$ $0 + 5 = x - 5 + 5$
Simplify equation: This simplifies to: $5 = x$

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\newline

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