To find $f(a + h)$ for the function $f(x) = 2x^2 - x + 3$, you substitute $a + h$ for $x$ in the function:

$f(a + h) = 2(a + h)^2 - (a + h) + 3$

Now, let's expand and simplify it:

1. Expand $(a + h)^2$: $(a + h)^2 = a^2 + 2ah + h^2$

2. Substitute this into the function: $f(a + h) = 2(a^2 + 2ah + h^2) - (a + h) + 3$

3. Distribute the 2: $f(a + h) = 2a^2 + 4ah + 2h^2 - a - h + 3$

So the final expression for $f(a + h)$ is:

$f(a + h) = 2a^2 + 4ah + 2h^2 - a - h + 3$

Would you like to go over any particular details or have any further questions?

Here are 5 related questions for further exploration:

1. What is the value of $f(2)$ if $f(x) = 2x^2 - x + 3$?
2. How would you find $f(a) + f(h)$ for the same function?
3. What is the derivative of $f(x) = 2x^2 - x + 3$?
4. How does the value of $h$ affect the expression $f(a + h)$?
5. What is the second derivative of the function $f(x) = 2x^2 - x + 3$?

Tip: When substituting expressions into functions, always expand and simplify to ensure clarity in your results.