f(x)=(x-8)^(2)-9 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=-11,x=5 (B) x=11,x=5 (c) x=11,x=-5 (D) f(x) does not intersect the x-axis.

Set equation to zero: To find the x-intercepts of the function, we need to set f(x) to zero and solve for x. So, we set the equation (x-8)² - 9 = 0.Isolate squared term: Now we solve the equation (x-8)² - 9 = 0 by adding 9 to both sides to isolate the squared term. (x-8)² = 9Take square root: Next, we take the square root of both sides of the equation to solve for x. x - 8 = ±√9Two solutions for x: Since the square root of 9 is 3, we have two solutions for x: x - 8 = 3 or x - 8 = -3Solve for x: Solving the first equation x - 8 = 3 for x gives us: x = 3 + 8 x = 11Solve for x: Solving the second equation x - 8 = -3 for x gives us: x = -3 + 8 x = 5Intersect x-axis: We have found two x-values where the graph of the function intersects the x-axis: x = 11 and x = 5. These correspond to choice (B).

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f(x)=(x-8)^(2)-9
At what values of
x does the graph of the function intersect the
x-axis?
Choose 1 answer:
(A)
x=-11,x=5
(B)
x=11,x=5
(c)
x=11,x=-5
(D)
f(x) does not intersect the
x-axis.

$f(x)=(x-8)^{2}-9$ $\newline$ At what values of $x$ does the graph of the function intersect the $x$ -axis? $\newline$ Choose $1$ answer: $\newline$ (A) $x=-11, x=5$ $\newline$ (B) $x=11, x=5$ $\newline$ (C) $x=11, x=-5$ $\newline$ (D) $f(x)$ does not intersect the $x$ -axis.

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Algebra 1

Domain and range of quadratic functions: equations

Full solution

f(x)=(x-8)^{2}-9

\newline

At what values of

x

does the graph of the function intersect the

x

-axis?

\newline

Choose

1

answer:

\newline

(A)

x=-11, x=5

\newline

(B)

x=11, x=5

\newline

(C)

x=11, x=-5

\newline

(D)

f(x)

does not intersect the

x

-axis.

Set equation to zero: To find the x-intercepts of the function, we need to set $f(x)$ to zero and solve for $x$ . $\newline$ So, we set the equation $(x-8)^2 - 9 = 0$ .
Isolate squared term: Now we solve the equation $(x-8)^2 - 9 = 0$ by adding $9$ to both sides to isolate the squared term. $\newline$ $(x-8)^2 = 9$
Take square root: Next, we take the square root of both sides of the equation to solve for x. $\newline$ $x - 8 = \pm\sqrt{9}$
Two solutions for x: Since the square root of $9$ is $3$ , we have two solutions for $x$ : $\newline$ $x - 8 = 3 \text{ or } x - 8 = -3$
Solve for x: Solving the first equation $x - 8 = 3$ for $x$ gives us: $\newline$ $x = 3 + 8$ $\newline$ $x = 11$
Solve for x: Solving the second equation $x - 8 = -3$ for $x$ gives us: $\newline$ $x = -3 + 8$ $\newline$ $x = 5$
Intersect x-axis: We have found two x-values where the graph of the function intersects the x-axis: $x = 11$ and $x = 5$ . $\newline$ These correspond to choice $(B)$ .