Math Problem Statement

if f (x) +4x^2 - 3x + 7 what is f(-2)

Solution

Given the function:

f(x)=4x23x+7f(x) = 4x^2 - 3x + 7

We want to find f(2)f(-2).

  1. Substitute x=2x = -2 into the function:

f(2)=4(2)23(2)+7f(-2) = 4(-2)^2 - 3(-2) + 7

  1. Calculate each term:

(2)2=4so4(2)2=4×4=16(-2)^2 = 4 \quad \text{so} \quad 4(-2)^2 = 4 \times 4 = 16 3(2)=6-3(-2) = 6

Now, combine all terms:

f(2)=16+6+7=29f(-2) = 16 + 6 + 7 = 29

Thus, f(2)=29f(-2) = 29.

Would you like more details on any of the steps?


Here are 5 related questions:

  1. What is f(0)f(0) for the same function?
  2. How would you find the roots of f(x)=0f(x) = 0?
  3. What is the derivative of f(x)=4x23x+7f(x) = 4x^2 - 3x + 7?
  4. How would you calculate f(1)f(1)?
  5. Can you express f(x)f(x) in vertex form?

Tip: Always simplify powers and multiplication before dealing with signs when substituting values into functions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Evaluation
Quadratic Functions

Formulas

f(x) = ax^2 + bx + c
Substitution of x into a function

Theorems

Basic principles of function evaluation

Suitable Grade Level

Grades 8-10