 f, of, x, equals, 2, x, squared, plus, 3, xf(x)=2x 
2
 +3x, find f, of, minus, 5f(−5)

To find \( f(-5) \) for the function \( f(x) = 2x^2 + 3x \), we need to substitute \( x = -5 \) into the function:

\[
f(-5) = 2(-5)^2 + 3(-5)
\]

Now, let's calculate step by step:

1. Calculate \( (-5)^2 \):
   \[
   (-5)^2 = 25
   \]

2. Multiply by 2:
   \[
   2 \times 25 = 50
   \]

3. Multiply 3 by -5:
   \[
   3 \times (-5) = -15
   \]

4. Add these results together:
   \[
   50 + (-15) = 35
   \]

Thus, \( f(-5) = 35 \).

Would you like more details on this, or do you have any questions?

Here are 5 related questions to consider:

1. How would you find \( f(x) \) if the function was \( f(x) = 2x^2 - 3x + 1 \)?
2. What happens to \( f(x) \) if the coefficients of the function change sign?
3. How do you determine the vertex of a quadratic function like \( f(x) = 2x^2 + 3x \)?
4. What is the significance of the discriminant in a quadratic equation?
5. How do you graph \( f(x) = 2x^2 + 3x \)?

**Tip:** When substituting negative values into functions, be extra careful with signs, especially when dealing with exponents and multiplications.

Learn how to evaluate the function f(x) = 2x^2 + 3x at x = -5 with step-by-step calculations. This problem covers quadratic equations, function evaluation, and substitution. Suitable for Grades 7-9.

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