f(x)=(x+2)^(2)-16 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=2,x=-6 (B) x=2,x=6 (c) x=-2,x=-6 (D) f(x) does not intersect the x-axis.

Problem: The question_prompt: At what values of x does the graph of the function f(x) = (x+2)² - 16 intersect the x-axis?Step 1: To find the x-intercepts of the function, we need to set f(x) to zero and solve for x. 0 = (x+2)² - 16Step 2: We can solve the equation by factoring the right side as a difference of squares: 0 = [(x+2) + 4][(x+2) - 4]Step 3: This gives us two factors: (x+2) + 4 = 0 or (x+2) - 4 = 0Step 4: Solving each equation for x gives us the x-intercepts: x+2+4=0 leads to x=-6 x+2-4=0 leads to x=2Solution: We have found the two x-intercepts of the function, which are x = -6 and x = 2.

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f(x)=(x+2)^(2)-16
At what values of
x does the graph of the function intersect the
x-axis?
Choose 1 answer:
(A)
x=2,x=-6
(B)
x=2,x=6
(c)
x=-2,x=-6
(D)
f(x) does not intersect the
x-axis.

$f(x)=(x+2)^{2}-16$ $\newline$ At what values of $x$ does the graph of the function intersect the $x$ -axis? $\newline$ Choose $1$ answer: $\newline$ (A) $x=2, x=-6$ $\newline$ (B) $x=2, x=6$ $\newline$ (C) $x=-2, x=-6$ $\newline$ (D) $f(x)$ does not intersect the $x$ -axis.

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Algebra 1

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Full solution

f(x)=(x+2)^{2}-16

\newline

At what values of

x

does the graph of the function intersect the

x

-axis?

\newline

Choose

1

answer:

\newline

(A)

x=2, x=-6

\newline

(B)

x=2, x=6

\newline

(C)

x=-2, x=-6

\newline

(D)

f(x)

does not intersect the

x

-axis.

Problem: The question_prompt: At what values of $x$ does the graph of the function $f(x) = (x+2)^2 - 16$ intersect the $x$ -axis?
Step $1$ : To find the x-intercepts of the function, we need to set $f(x)$ to zero and solve for $x$ . $0 = (x+2)^2 - 16$
Step $2$ : We can solve the equation by factoring the right side as a difference of squares: $\newline$ $0 = [(x+2) + 4][(x+2) - 4]$
Step $3$ : This gives us two factors: $\newline$ $(x+2) + 4 = 0$ or $(x+2) - 4 = 0$
Step $4$ : Solving each equation for x gives us the x-intercepts: $\newline$ $x+2+4=0$ leads to $x=-6$ $\newline$ $x+2-4=0$ leads to $x=2$
Solution: We have found the two $x$ -intercepts of the function, which are $x = -6$ and $x = 2$ .