Question

Find the​ x-intercept(s) of the graph of the equation. Use the​ x-intercepts to match the equation to its graph.
y equals negative left parenthesis x minus 1 right parenthesis squared plus 9
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Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The​ x-intercept(s) is/are xequals
  
enter your response here.
​(Simplify your answer. Use a comma to separate answers as​ needed.)
B.
There are no intercepts.

Answer 1

To find the \( x \)-intercept(s) of the graph of the equation \( y = - (x - 1)^2 + 9 \), we need to set \( y \) equal to zero and solve for \( x \).

1. Set \( y = 0 \):
\[
0 = - (x - 1)^2 + 9
\]

2. Rearrange the equation:
\[
(x - 1)^2 = 9
\]

3. Take the square root of both sides:
\[
x - 1 = 3 \quad \text{or} \quad x - 1 = -3
\]

4. Solve for \( x \):
- For \( x - 1 = 3 \):
\[
x = 4
\]
- For \( x - 1 = -3 \):
\[
x = -2
\]

Thus, the \( x \)-intercepts are \( x = -2 \) and \( x = 4 \).

To summarize, the answer is:
A. The \(\ x \)-intercept(s) is/are \( x = -2, 4 \).