Discover a wealth of information and get your questions answered on IDNLearn.com. Discover reliable and timely information on any topic from our network of experienced professionals.

Plot the [tex]\( x \)[/tex]-intercept of the function [tex]\( f(x) = (x + 4)^2 \)[/tex].

[tex]\[
\begin{tabular}{|l|l|}
\hline
x & y \\
\hline
& \\
& \\
& \\
\hline
\end{tabular}
\][/tex]

Click or tap the graph to plot a point.


Sagot :

To find the [tex]\( x \)[/tex]-intercept of the function [tex]\( f(x) = (x + 4)^2 \)[/tex], we follow these steps:

1. Understand the definition of the [tex]\( x \)[/tex]-intercept: The [tex]\( x \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( x \)[/tex]-axis. This means the [tex]\( y \)[/tex]-value at the [tex]\( x \)[/tex]-intercept is 0.

2. Set the function equal to zero: To find the [tex]\( x \)[/tex]-intercept, we need to solve the equation where the function [tex]\( f(x) \)[/tex] is equal to zero:
[tex]\[ (x + 4)^2 = 0 \][/tex]

3. Solve for [tex]\( x \)[/tex]:
[tex]\[ (x + 4)^2 = 0 \][/tex]
Taking the square root of both sides, we get:
[tex]\[ x + 4 = 0 \][/tex]
Solving for [tex]\( x \)[/tex], we find:
[tex]\[ x = -4 \][/tex]

4. Substitute [tex]\( x \)[/tex] back into the function to verify: To ensure our solution, we substitute [tex]\( -4 \)[/tex] back into the function:
[tex]\[ f(-4) = (-4 + 4)^2 = 0 \][/tex]
Indeed, the [tex]\( y \)[/tex]-value at [tex]\( x = -4 \)[/tex] is 0.

5. Record the intercept: Therefore, the [tex]\( x \)[/tex]-intercept of the function [tex]\( f(x) = (x + 4)^2 \)[/tex] is [tex]\( (-4, 0) \)[/tex].

Now, let's plot this intercept on the graph:
[tex]\[ \begin{tabular}{|l|l|} \hline $x$ & $y$ \\ \hline -4 & 0 \\ \hline & \\ \hline & \\ \hline & \\ \hline \end{tabular} \][/tex]

Click or tap on the graph at the point [tex]\((-4, 0)\)[/tex] to plot the [tex]\( x \)[/tex]-intercept.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.