https://file.aiquickdraw.com/mathbot/file/1727346826190qyr1cscv.jpg

Let's analyze the problem. The equation given is:

\[
y = (x - 1)^2 - 4
\]

To find the x-intercepts, we set \( y = 0 \) and solve for \( x \):

\[
0 = (x - 1)^2 - 4
\]

1. Add 4 to both sides:

\[
4 = (x - 1)^2
\]

2. Take the square root of both sides:

\[
x - 1 = \pm 2
\]

3. Solve for \( x \):

- \( x - 1 = 2 \implies x = 3 \)
- \( x - 1 = -2 \implies x = -1 \)

So, the x-intercepts are \( x = 3 \) and \( x = -1 \).

The correct answer is option **2**: "The graph intercepts the x-axis at 3 and -1."

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you find the y-intercept of a quadratic equation?
2. What does the vertex of the equation \( y = (x - 1)^2 - 4 \) represent?
3. How can you rewrite \( y = (x - 1)^2 - 4 \) in standard form?
4. What is the axis of symmetry for the graph of \( y = (x - 1)^2 - 4 \)?
5. How does the graph of \( y = (x - 1)^2 - 4 \) compare to \( y = x^2 \)?

**Tip**: When finding x-intercepts, always set \( y = 0 \) and solve for \( x \).

Use a graphing calculator to determine the x intercepts of the graph y = (x - 1)^2 - 4.

Learn how to find the x-intercepts of the quadratic function y = (x - 1)^2 - 4 by solving the equation step by step. This involves algebraic techniques such as setting y = 0 and using the zero-product property. Suitable for students in Grades 8-10.

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