Given f, of, x, equals, minus, 3, x, squared, plus, 10, x, plus, 13*f*(*x*)=−3*x*2+10*x*+13, find f, of, minus, 1*f*(−1)

To find \( f(-1) \) given the function \( f(x) = -3x^2 + 10x + 13 \), you need to substitute \( x = -1 \) into the function.

### Step-by-Step Solution:

1. Start with the function:
   \[
   f(x) = -3x^2 + 10x + 13
   \]

2. Substitute \( x = -1 \) into the function:
   \[
   f(-1) = -3(-1)^2 + 10(-1) + 13
   \]

3. Calculate each term:
   - \( (-1)^2 = 1 \)
   - \( -3 \times 1 = -3 \)
   - \( 10 \times (-1) = -10 \)
   - \( 13 \) remains as is.

4. Combine these values:
   \[
   f(-1) = -3 - 10 + 13
   \]

5. Simplify:
   \[
   f(-1) = -13 + 13 = 0
   \]

So, \( f(-1) = 0 \).

Would you like a detailed explanation or have any questions? Here are some related questions you might consider:

1. How would the result change if \( x = 2 \)?
2. What is the vertex of the parabola represented by \( f(x) \)?
3. How can you determine the x-intercepts of \( f(x) \)?
4. What is the axis of symmetry for the function \( f(x) \)?
5. How does the sign of the coefficient of \( x^2 \) affect the shape of the graph?

**Tip:** Always double-check your substitutions and arithmetic when working with functions to avoid simple mistakes.

Learn how to find f(-1) given the quadratic function f(x) = -3x^2 + 10x + 13 with a step-by-step solution. This problem involves substituting x = -1 into the function and performing arithmetic operations. Suitable for students in Grades 7-9.

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