Math Problem Statement

Given f(x) = -x^2 - 8x + 8, find f(-5)

Solution

The function provided is:

f(x)=x28x+8f(x) = -x^2 - 8x + 8

We are asked to find f(5)f(-5).

To do this, we substitute x=5x = -5 into the function:

f(5)=(5)28(5)+8f(-5) = -(-5)^2 - 8(-5) + 8

First, calculate each term:

  1. (5)2=25(-5)^2 = 25
  2. (5)2=25-(-5)^2 = -25
  3. 8(5)=40-8(-5) = 40

Now, substitute the values:

f(5)=25+40+8=23f(-5) = -25 + 40 + 8 = 23

Thus, f(5)=23f(-5) = 23.

Would you like more details or further clarification?

Here are 5 related questions for practice:

  1. Find f(2)f(2) for the same function f(x)=x28x+8f(x) = -x^2 - 8x + 8.
  2. What is the vertex of the parabola defined by f(x)=x28x+8f(x) = -x^2 - 8x + 8?
  3. Determine the x-intercepts of f(x)=x28x+8f(x) = -x^2 - 8x + 8.
  4. How would you rewrite f(x)=x28x+8f(x) = -x^2 - 8x + 8 in vertex form?
  5. What is the axis of symmetry for the function f(x)=x28x+8f(x) = -x^2 - 8x + 8?

Tip: When evaluating functions, always double-check your substitutions for accuracy!

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Substitution in Functions

Formulas

f(x) = ax^2 + bx + c
Substitution f(a) = -a^2 - 8a + 8

Theorems

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Suitable Grade Level

Grades 8-10