Determine the x-intercepts of the equation y = x^2 - 4.

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Question: Determine the x-intercepts of the equation y = x^2 - 4.

Options:

Correct Answer: x = 2, -2

Solution:

Set y = 0: x^2 - 4 = 0. Factoring gives (x - 2)(x + 2) = 0. Thus, x = 2 and x = -2.

Determine the x-intercepts of the equation y = x^2 - 4.

Determine the x-intercepts of the equation y = x^2 - 4.

Step 1: Start with the equation y = x^2 - 4.
Step 2: To find the x-intercepts, set y equal to 0. This gives you the equation 0 = x^2 - 4.
Step 3: Rearrange the equation to x^2 - 4 = 0.
Step 4: Factor the equation. The expression x^2 - 4 can be factored into (x - 2)(x + 2) = 0.
Step 5: Set each factor equal to 0. This gives you two equations: x - 2 = 0 and x + 2 = 0.
Step 6: Solve the first equation x - 2 = 0. This gives x = 2.
Step 7: Solve the second equation x + 2 = 0. This gives x = -2.
Step 8: The x-intercepts are the points where the graph crosses the x-axis, which are x = 2 and x = -2.

Quadratic Equations – Understanding how to find x-intercepts by setting the equation to zero and solving for x.
Factoring – Applying factoring techniques to solve quadratic equations.