Math Problem Statement

solve it by using the value of x -1

Solution

To solve the function f(x)=x2+2x2f(x) = x^2 + 2x - 2 at x=1x = -1, we substitute x=1x = -1 into the function:

f(1)=(1)2+2(1)2f(-1) = (-1)^2 + 2(-1) - 2

Now, let's calculate this step by step:

  1. (1)2=1(-1)^2 = 1
  2. 2(1)=22(-1) = -2
  3. Therefore, f(1)=122f(-1) = 1 - 2 - 2

Simplifying further:

f(1)=14=3f(-1) = 1 - 4 = -3

So, the value of the function f(x)f(x) when x=1x = -1 is f(1)=3f(-1) = -3.

Would you like further details on this calculation, or do you have any other questions?

Here are 8 related questions:

  1. What is the function value at x=0x = 0?
  2. How does the value change if x=1x = 1?
  3. Can you find the derivative of f(x)f(x) and evaluate it at x=1x = -1?
  4. What is the significance of the vertex of the parabola represented by f(x)f(x)?
  5. How would the function behave for very large positive or negative values of xx?
  6. What are the roots of the function f(x)=0f(x) = 0?
  7. How would you rewrite f(x)f(x) by completing the square?
  8. What is the range of the function f(x)f(x)?

Tip: Evaluating functions at specific points is a common way to understand their behavior locally, especially when analyzing graphs.

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Math Problem Analysis

Mathematical Concepts

Function evaluation
Quadratic functions

Formulas

Quadratic function formula f(x) = ax^2 + bx + c

Theorems

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Suitable Grade Level

Grades 9-12