https://file.aiquickdraw.com/mathbot/file/1726179363185zed8hxzj.jpg

The given equation from the image is:

\[
p(x) = (x + 7)^2 - 15
\]

You mentioned that \( x = 5 \), so we will substitute \( x = 5 \) into the equation and solve for \( p(5) \).

Let's calculate it step by step:

\[
p(5) = (5 + 7)^2 - 15
\]

Now, simplifying inside the parentheses:

\[
p(5) = (12)^2 - 15
\]

Next, square the 12:

\[
p(5) = 144 - 15
\]

Finally, subtract 15 from 144:

\[
p(5) = 129
\]

So, the value of \( p(5) \) is 129.

Would you like further details or have any questions?

Here are some related questions to expand on this concept:

1. What happens to the function if \( x = -7 \)?
2. How can you find the vertex of the quadratic function \( p(x) = (x + 7)^2 - 15 \)?
3. What are the roots (solutions) of the equation \( p(x) = 0 \)?
4. How does the graph of this quadratic function look like?
5. What is the general form of a quadratic function, and how does it relate to this one?

**Tip:** For quadratic functions in the form \( (x + a)^2 + b \), the vertex of the parabola is at the point \( (-a, b) \).

Learn how to solve the quadratic function p(x) = (x + 7)^2 - 15 by substituting x = 5. This problem demonstrates function evaluation and basic algebraic operations. Ideal for students in Grades 8-10.

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