Math Problem Statement

Given f, of, x, equals, minus, 3, x, squaredf(x)=−3x2, find f, of, minus, 10f(−10)

Solution

Given the function f(x)=3x2f(x) = -3x^2, to find f(10)f(-10), you need to substitute x=10x = -10 into the function.

Step-by-Step Solution:

  1. Start with the function: f(x)=3x2f(x) = -3x^2

  2. Substitute x=10x = -10 into the function: f(10)=3(10)2f(-10) = -3(-10)^2

  3. Calculate the square of 10-10: (10)2=100(-10)^2 = 100

  4. Multiply by 3-3: f(10)=3×100=300f(-10) = -3 \times 100 = -300

So, f(10)=300f(-10) = -300.

Would you like more details or have any questions? Here are some related questions you might consider:

  1. What would f(10)f(10) be?
  2. How does the function behave as xx increases or decreases?
  3. What is the value of f(0)f(0)?
  4. How would the function change if the coefficient of x2x^2 were positive?
  5. What is the general form of a quadratic function like this one?

Tip: Remember that squaring a negative number always results in a positive value, but the negative sign outside the square still affects the overall result.

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations

Formulas

Quadratic equation formula ax^2 + bx + c = 0

Theorems

None

Suitable Grade Level

Grades 9-12