Questions: Find the intercept(s) of the following equation. y=x^2-4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are . (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

Find the intercept(s) of the following equation. y=x^2-4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are . (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.
Transcript text: Find the intercept(s) of the following equation. \[ y=x^{2}-4 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are $\square$ . (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.
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Solution

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Solution Steps

Step 1: Find the y-intercept

To find the y-intercept, set \( x = 0 \) in the equation \( y = x^2 - 4 \).

\[ y = 0^2 - 4 = -4 \]

Thus, the y-intercept is the point \((0, -4)\).

Step 2: Find the x-intercepts

To find the x-intercepts, set \( y = 0 \) in the equation \( y = x^2 - 4 \) and solve for \( x \).

\[ 0 = x^2 - 4 \]

\[ x^2 = 4 \]

\[ x = \pm 2 \]

Thus, the x-intercepts are the points \((-2, 0)\) and \((2, 0)\).

Final Answer

The intercepts of the equation \( y = x^2 - 4 \) are:

\[ \boxed{(0, -4), (-2, 0), (2, 0)} \]

The correct choice is A.

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