Math Problem Statement

When x=-3 what how do you evaluate the function f(x)=-x^2+5

Solution

To evaluate the function f(x)=x2+5f(x) = -x^2 + 5 when x=3x = -3, follow these steps:

  1. Substitute x=3x = -3 into the function: f(3)=(3)2+5f(-3) = -(-3)^2 + 5

  2. First, calculate (3)2(-3)^2, which is 99: f(3)=9+5f(-3) = -9 + 5

  3. Now, add 9-9 and 55: f(3)=4f(-3) = -4

So, when x=3x = -3, the value of the function is f(3)=4f(-3) = -4.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:

  1. What is the vertex of the function f(x)=x2+5f(x) = -x^2 + 5?
  2. How do you determine the domain and range of f(x)=x2+5f(x) = -x^2 + 5?
  3. What happens to f(x)=x2+5f(x) = -x^2 + 5 when x=0x = 0?
  4. Can you explain how the graph of f(x)=x2+5f(x) = -x^2 + 5 looks?
  5. How do you solve f(x)=0f(x) = 0 for f(x)=x2+5f(x) = -x^2 + 5?

Tip: In quadratic functions like f(x)=x2+5f(x) = -x^2 + 5, the negative sign in front of x2x^2 flips the parabola downward.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Function Evaluation

Formulas

f(x) = -x^2 + 5

Theorems

Basic function evaluation
Properties of quadratic functions

Suitable Grade Level

Grades 7-9