To solve the problem, we will substitute the given values into the function \( h(x) = 2x^2 - x + 3 \).

1. **Find \( h(3) \):**
   \[
   h(3) = 2(3)^2 - 3 + 3 = 2(9) - 3 + 3 = 18 - 3 + 3 = 18
   \]

2. **Find \( h(2-) \):**
   If by \( h(2-) \), you mean approaching \( x = 2 \) from the left side (left-hand limit), the function \( h(x) \) is continuous and does not have a discontinuity at \( x = 2 \), so we can directly substitute \( x = 2 \):
   \[
   h(2) = 2(2)^2 - 2 + 3 = 2(4) - 2 + 3 = 8 - 2 + 3 = 9
   \]
   Hence, \( h(2-) = h(2) = 9 \).

3. **Find \( h(x+1) \):**
   Substituting \( x+1 \) into the function:
   \[
   h(x+1) = 2(x+1)^2 - (x+1) + 3
   \]
   First, expand \( (x+1)^2 \):
   \[
   (x+1)^2 = x^2 + 2x + 1
   \]
   Now, substitute back into the equation:
   \[
   h(x+1) = 2(x^2 + 2x + 1) - (x+1) + 3 = 2x^2 + 4x + 2 - x - 1 + 3
   \]
   Simplify:
   \[
   h(x+1) = 2x^2 + 3x + 4
   \]

So, the results are:
- \( h(3) = 18 \)
- \( h(2-) = 9 \)
- \( h(x+1) = 2x^2 + 3x + 4 \)

Would you like any further details on these calculations?

### Relative questions:
1. What is the value of \( h(4) \)?
2. How would you find \( h(0) \)?
3. What does it mean for a function to have a left-hand limit like \( h(2-) \)?
4. Can you derive the general form of \( h(x-1) \)?
5. How does the quadratic nature of the function \( h(x) \) affect its graph?

### Tip:
For polynomial functions like \( h(x) \), continuity means the left-hand and right-hand limits will always be the same at any point.

h(x) = 2x² - x + 3 find h(3), h(2-), h(x+1)

Learn how to evaluate the quadratic function h(x) = 2x² - x + 3 by finding h(3), h(2-) and h(x+1). This step-by-step guide covers key algebraic concepts, limits, and function evaluation, suitable for students in Grades 9-11.

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