Given f, of, x, equals, 3, x, squared, plus, 9, x, minus, 16*f*(*x*)=3*x*2+9*x*−16, find f, of, minus, 8*f*(−8)

To find \( f(-8) \) for the function \( f(x) = 3x^2 + 9x - 16 \), follow these steps:

### Step 1: Substitute \( x = -8 \) into the function \( f(x) \).

\[
f(-8) = 3(-8)^2 + 9(-8) - 16
\]

### Step 2: Simplify the expression.

- First, calculate \( (-8)^2 \):

  \[
  (-8)^2 = 64
  \]

- Now, substitute \( 64 \) into the expression:

  \[
  f(-8) = 3(64) + 9(-8) - 16
  \]

- Multiply the terms:

  \[
  f(-8) = 192 - 72 - 16
  \]

- Finally, add and subtract the terms:

  \[
  f(-8) = 192 - 88 = 104
  \]

So, \( f(-8) = 104 \).

Would you like more details or have any questions about this process?

Here are some related questions:

1. How do you find the vertex of the quadratic function \( f(x) = 3x^2 + 9x - 16 \)?
2. What are the roots of the equation \( 3x^2 + 9x - 16 = 0 \)?
3. How does the discriminant help in determining the nature of the roots for \( f(x) = 3x^2 + 9x - 16 \)?
4. What is the axis of symmetry for the function \( f(x) = 3x^2 + 9x - 16 \)?
5. Can you graph the function \( f(x) = 3x^2 + 9x - 16 \) and describe its shape?

**Tip:** When evaluating a quadratic function, always handle the square and multiplication operations carefully to avoid errors in sign and magnitude.

Learn how to evaluate the function f(x) = 3x^2 + 9x - 16 at x = -8 step-by-step with a detailed solution. This problem involves quadratic equations and arithmetic operations, focusing on evaluating functions at specific points. Suitable for students in Grades 7-9.

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