Let ​g(x)equals
2xsquaredplus5xplus7. 
Find ​g(pplus
4
​).
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Part 1
​g(pplus
4​)equalsenter your response here
​(Simplify your​ answer.)

The function \( g(x) = 2x^2 + 5x + 7 \) is given. You are asked to find \( g(p + 4) \), which means substituting \( p + 4 \) for \( x \) in the function \( g(x) \).

Here’s how to do it:

1. Start with the given function:
   \[
   g(x) = 2x^2 + 5x + 7
   \]

2. Substitute \( p + 4 \) for \( x \):
   \[
   g(p + 4) = 2(p + 4)^2 + 5(p + 4) + 7
   \]

3. Expand \( (p + 4)^2 \):
   \[
   (p + 4)^2 = p^2 + 8p + 16
   \]

4. Now, substitute this back into the equation:
   \[
   g(p + 4) = 2(p^2 + 8p + 16) + 5(p + 4) + 7
   \]

5. Distribute the 2:
   \[
   g(p + 4) = 2p^2 + 16p + 32 + 5(p + 4) + 7
   \]

6. Distribute the 5:
   \[
   g(p + 4) = 2p^2 + 16p + 32 + 5p + 20 + 7
   \]

7. Combine like terms:
   \[
   g(p + 4) = 2p^2 + (16p + 5p) + (32 + 20 + 7)
   \]
   \[
   g(p + 4) = 2p^2 + 21p + 59
   \]

Thus, the simplified expression for \( g(p + 4) \) is:
\[
g(p + 4) = 2p^2 + 21p + 59
\]

Let me know if you want more details or have any questions!

Here are 5 related questions:
1. What would \( g(p-3) \) be?
2. How would you find \( g(2p) \)?
3. Can you graph the function \( g(x) = 2x^2 + 5x + 7 \)?
4. How does changing the value of \( x \) affect the function \( g(x) \)?
5. How do you solve for \( x \) when \( g(x) = 0 \)?

**Tip:** Always simplify expressions by expanding and combining like terms step by step to avoid mistakes.

Let g(x) equals 2x^2 + 5x + 7. Find g(p + 4). (Simplify your answer.)

Learn how to simplify the expression g(p + 4) for the function g(x) = 2x^2 + 5x + 7 using substitution and polynomial expansion. This solution provides a detailed step-by-step process, ideal for students in Grades 8-10.

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