f(x)=(x+6)^(2)-49 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=1,x=13 (B) x=-1,x=-13 (C) x=1,x=-13 (D) f(x) does not intersect the x-axis.

Set f(x) to zero: To find the x-intercepts of the function, we need to set f(x) to zero and solve for x. f(x) = (x+6)^2 - 49 = 0Factor and solve: Now we solve the equation (x+6)^2 - 49 = 0 by factoring it as a difference of squares. (x+6+7)(x+6-7) = 0 (x+13)(x-1) = 0Solve for x: We have two factors, so we set each factor equal to zero and solve for x. x+13 = 0 or x-1 = 0x = -13: Solving the first equation for x gives us: x = -13x = 1: Solving the second equation for x gives us: x = 1Intersecting x-axis: We have found the two x-values where the graph of the function intersects the x-axis: x = -13 and x = 1.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

f(x)=(x+6)^(2)-49
At what values of
x does the graph of the function intersect the
x-axis?
Choose 1 answer:
(A)
x=1,x=13
(B)
x=-1,x=-13
(C)
x=1,x=-13
(D)
f(x) does not intersect the
x-axis.

$f(x)=(x+6)^{2}-49$ $\newline$ At what values of $x$ does the graph of the function intersect the $x$ -axis? $\newline$ Choose $1$ answer: $\newline$ (A) $x=1, x=13$ $\newline$ (B) $x=-1, x=-13$ $\newline$ (C) $x=1, x=-13$ $\newline$ (D) $f(x)$ does not intersect the $x$ -axis.

View step-by-step help

Home

Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

f(x)=(x+6)^{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=1, x=13

\newline

(B)

x=-1, x=-13

\newline

(C)

x=1, x=-13

\newline

(D)

f(x)

does not intersect the

x

-axis.

Set $f(x)$ to zero: To find the x-intercepts of the function, we need to set $f(x)$ to zero and solve for $x$ . $\newline$ $f(x) = (x+6)^2 - 49 = 0$
Factor and solve: Now we solve the equation $(x+6)^2 - 49 = 0$ by factoring it as a difference of squares. $(x+6+7)(x+6-7) = 0$ $(x+13)(x-1) = 0$
Solve for x: We have two factors, so we set each factor equal to zero and solve for x. $\newline$ $x+13 = 0$ or $x-1 = 0$
{