Let's find $p(x+1)$ for the function $p(x) = 2x^2 + 5x - 3$.

Step 1: Substitute $x+1$ into $p(x)$

$p(x+1) = 2(x+1)^2 + 5(x+1) - 3$

Step 2: Expand the square term

$(x+1)^2 = x^2 + 2x + 1$

Step 3: Substitute and expand

$p(x+1) = 2(x^2 + 2x + 1) + 5(x+1) - 3$ $p(x+1) = 2x^2 + 4x + 2 + 5x + 5 - 3$

Step 4: Combine like terms

$p(x+1) = 2x^2 + 9x + 4$

So, $p(x+1) = \boxed{2x^2 + 9x + 4}$.

Would you like any further details or have any questions?

Here are some related questions:

1. What is $p(x-1)$ for the same function $p(x) = 2x^2 + 5x - 3$?
2. How would $p(x+2)$ look for $p(x)$?
3. What are the roots of the function $p(x+1)$?
4. Can you find the vertex of the parabola described by $p(x+1)$?
5. How does $p(x+1)$ compare to $p(x)$ in terms of its graph?

Tip: When substituting expressions into functions, expand carefully and combine like terms to ensure accuracy.