To solve the expression \( 2f(-3) - f(4) \) for the function \( f(x) = 3x^2 - x + 5 \), follow these steps:

### Step 1: Evaluate \( f(-3) \)
Substitute \( x = -3 \) into the function:
\[
f(-3) = 3(-3)^2 - (-3) + 5 = 3(9) + 3 + 5 = 27 + 3 + 5 = 35
\]

### Step 2: Evaluate \( f(4) \)
Substitute \( x = 4 \) into the function:
\[
f(4) = 3(4)^2 - 4 + 5 = 3(16) - 4 + 5 = 48 - 4 + 5 = 49
\]

### Step 3: Compute \( 2f(-3) - f(4) \)
Now use the values found in Steps 1 and 2:
\[
2f(-3) - f(4) = 2(35) - 49 = 70 - 49 = 21
\]

### Final Answer:
\[
2f(-3) - f(4) = 21
\]

Would you like any additional details on these steps?

Here are five related questions:
1. How would you find the derivative of \( f(x) = 3x^2 - x + 5 \)?
2. What happens to the expression if \( f(x) \) changes to a different quadratic function?
3. How would the process change if you were given \( 3f(-3) - 2f(4) \)?
4. How do you solve for \( x \) when \( f(x) = 0 \) for this function?
5. Can you generalize \( 2f(a) - f(b) \) for any values of \( a \) and \( b \)?

**Tip:** Always substitute values carefully and simplify step by step to avoid mistakes.

For f(x)=3x^2 – x+5, calculate 2f(–3) – f(4)

Learn how to solve 2f(–3) – f(4) for the quadratic function f(x) = 3x^2 – x + 5. This step-by-step guide shows how to evaluate quadratic functions and apply basic arithmetic operations. Ideal for students in Grades 9-10.

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