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In the function f(x) = x^2 - 4, what are the x-intercepts?

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Question: In the function f(x) = x^2 - 4, what are the x-intercepts?

Options:

  1. 2 and -2
  2. 4 and -4
  3. 0 and 4
  4. None

Correct Answer: 2 and -2

Solution: 

To find the x-intercepts, set f(x) = 0: x^2 - 4 = 0, which factors to (x - 2)(x + 2) = 0, giving x-intercepts at 2 and -2.

In the function f(x) = x^2 - 4, what are the x-intercepts?

Practice Questions

Q1
In the function f(x) = x^2 - 4, what are the x-intercepts?
  1. 2 and -2
  2. 4 and -4
  3. 0 and 4
  4. None

Questions & Step-by-Step Solutions

In the function f(x) = x^2 - 4, what are the x-intercepts?
  • Step 1: Start with the function f(x) = x^2 - 4.
  • Step 2: To find the x-intercepts, set f(x) equal to 0: x^2 - 4 = 0.
  • Step 3: Rearrange the equation to solve for x: x^2 - 4 = 0.
  • Step 4: Factor the equation: (x - 2)(x + 2) = 0.
  • Step 5: Set each factor equal to 0: x - 2 = 0 and x + 2 = 0.
  • Step 6: Solve each equation: x = 2 and x = -2.
  • Step 7: The x-intercepts are at the points (2, 0) and (-2, 0).
  • Quadratic Functions – Understanding the properties of quadratic functions, including how to find x-intercepts by solving the equation f(x) = 0.
  • Factoring – Applying factoring techniques to solve quadratic equations.
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