f(x)=(x-10)^(2)-49 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=17,x=3 (B) x=17,x=-3 (c) x=-17,x=3 (D) f(x) does not intersect the x-axis.

Problem Understanding: Understand the problem. The graph of a function intersects the x-axis where the function value f(x) is equal to 0. So we need to find the values of x for which f(x) = 0.Setting the Equation: Set the function equal to zero and solve for x. f(x) = (x - 10)^2 - 49 = 0Solving the Quadratic Equation: Solve the quadratic equation. (x - 10)^2 = 49 Take the square root of both sides: √((x - 10)^2) = ±√49 x - 10 = ±7Final Solution: Solve for x. x - 10 = 7 or x - 10 = -7 x = 17 or x = 3

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f(x)=(x-10)^(2)-49
At what values of
x does the graph of the function intersect the
x-axis?
Choose 1 answer:
(A)
x=17,x=3
(B)
x=17,x=-3
(c)
x=-17,x=3
(D)
f(x) does not intersect the
x-axis.

$f(x)=(x-10)^{2}-49$ $\newline$ At what values of $x$ does the graph of the function intersect the $x$ -axis? $\newline$ Choose $1$ answer: $\newline$ (A) $x=17, x=3$ $\newline$ (B) $x=17, x=-3$ $\newline$ (C) $x=-17, x=3$ $\newline$ (D) $f(x)$ does not intersect the $x$ -axis.

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Math Problems

Algebra 1

Transformations of absolute value functions: translations, reflections, and dilations

Full solution

f(x)=(x-10)^{2}-49

\newline

At what values of

x

does the graph of the function intersect the

x

-axis?

\newline

Choose

1

answer:

\newline

(A)

x=17, x=3

\newline

(B)

x=17, x=-3

\newline

(C)

x=-17, x=3

\newline

(D)

f(x)

does not intersect the

x

-axis.

Problem Understanding: Understand the problem. $\newline$ The graph of a function intersects the x-axis where the function value $f(x)$ is equal to $0$ . So we need to find the values of $x$ for which $f(x) = 0$ .
Setting the Equation: Set the function equal to zero and solve for x. $\newline$ f(x) = $(x - 10)^2 - 49 = 0$
Solving the Quadratic Equation: Solve the quadratic equation. $\newline$ $(x - 10)^2 = 49$ $\newline$ Take the square root of both sides: $\newline$ $\sqrt{(x - 10)^2} = \pm\sqrt{49}$ $\newline$ x - $10$ = \pm $7$
Final Solution: Solve for $x$ . $x - 10 = 7 \quad \text{or} \quad x - 10 = -7$ $x = 17 \quad \text{or} \quad x = 3$