f(x)=(x-7)^(2)-64 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=-15,x=-1 (B) x=15,x=1 (C) x=15,x=-1 (D) f(x) does not intersect the x-axis.

Setting up the equation: To find the x-intercepts of the function, we need to set f(x) to zero and solve for x. f(x) = (x-7)² - 64 = 0Moving 64 to the other side: Now we solve the equation (x-7)² - 64 = 0 by moving 64 to the other side of the equation. (x-7)² = 64Taking the square root: Next, we take the square root of both sides of the equation to solve for x. x - 7 = ±√64Positive square root solution: Since the square root of 64 is 8, we have two solutions for x. x - 7 = ±8Negative square root solution: Solving for x when we have the positive square root: x - 7 = 8 x = 8 + 7 x = 15Solving for x when we have the negative square root: x - 7 = -8 x = -8 + 7 x = -1

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f(x)=(x-7)^(2)-64
At what values of
x does the graph of the function intersect the
x-axis?
Choose 1 answer:
(A)
x=-15,x=-1
(B)
x=15,x=1
(C)
x=15,x=-1
(D)
f(x) does not intersect the
x-axis.

$f(x)=(x-7)^{2}-64$ $\newline$ At what values of $x$ does the graph of the function intersect the $x$ -axis? $\newline$ Choose $1$ answer: $\newline$ (A) $x=-15, x=-1$ $\newline$ (B) $x=15, x=1$ $\newline$ (C) $x=15, x=-1$ $\newline$ (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-7)^{2}-64

\newline

At what values of

x

does the graph of the function intersect the

x

-axis?

\newline

Choose

1

answer:

\newline

(A)

x=-15, x=-1

\newline

(B)

x=15, x=1

\newline

(C)

x=15, x=-1

\newline

(D)

f(x)

does not intersect the

x

-axis.

Setting up the equation: To find the $x$ -intercepts of the function, we need to set $f(x)$ to zero and solve for $x$ . $\newline$ $f(x) = (x-7)^2 - 64 = 0$
Moving $64$ to the other side: Now we solve the equation $(x-7)^2 - 64 = 0$ by moving $64$ to the other side of the equation. $\newline$ $(x-7)^2 = 64$
Taking the square root: Next, we take the square root of both sides of the equation to solve for x. $\newline$ $x - 7 = \pm\sqrt{64}$
Positive square root solution: Since the square root of $64$ is $8$ , we have two solutions for $x$ . $\newline$ $x - 7 = \pm 8$
Negative square root solution: Solving for $x$ when we have the positive square root: $x - 7 = 8$ $x = 8 + 7$ $x = 15$
Negative square root solution: Solving for $x$ when we have the positive square root: $x - 7 = 8$ $x = 8 + 7$ $x = 15$ Solving for $x$ when we have the negative square root: $x - 7 = -8$ $x = -8 + 7$ $x = -1$