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

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

Options:

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

Correct Answer: -2, 2

Solution: 

To find x-intercepts, set f(x) = 0: x^2 - 4 = 0, which gives x = ±2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If f(x) = x^2 - 4, what are the x-intercepts?
  • Step 1: Understand that x-intercepts are points where the graph of the function crosses the x-axis. This happens when f(x) = 0.
  • Step 2: Write down the function: f(x) = x^2 - 4.
  • Step 3: Set the function equal to zero to find the x-intercepts: x^2 - 4 = 0.
  • Step 4: Solve the equation x^2 - 4 = 0. This can be done by adding 4 to both sides: x^2 = 4.
  • Step 5: Take the square root of both sides. Remember that taking the square root gives two solutions: x = 2 and x = -2.
  • Step 6: Conclude that the x-intercepts are at the points (2, 0) and (-2, 0).
  • Finding x-intercepts – To find the x-intercepts of a function, set the function equal to zero and solve for x.
  • Quadratic equations – Understanding how to solve quadratic equations, particularly those in the form of x^2 - k = 0.
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