Find the following for the function.
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
\[
g(x)=-(x+6)^{2}+9
\]
(A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The $y$-intercept is -27 .
(Type an integer or decimal rounded to two decimal places as needed.)
B. There is no y-intercept.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The $x$-intercepts are $-9,-3$.
(Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as need
B. There is no x-intercept.
(B) Vertex:
(Type an ordered pair.)
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Answer
Final Answer: The y-intercept is \(\boxed{-27}\) and the x-intercepts are \(\boxed{-9}\) and \(\boxed{-3}\).
Step 1 ：The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when \(x = 0\).
Step 2 ：Substitute \(x = 0\) into the function \(g(x) = -(x+6)^2 + 9\) to find the y-intercept.
Step 3 ：The y-intercept is \(-27\).
Step 4 ：The x-intercepts of a function are the points where the graph of the function intersects the x-axis. This occurs when \(g(x) = 0\).
Step 5 ：Solve the equation \(g(x) = 0\) to find the x-intercepts.
Step 6 ：The x-intercepts are \(-9\) and \(-3\).
Step 7 ：Final Answer: The y-intercept is \(\boxed{-27}\) and the x-intercepts are \(\boxed{-9}\) and \(\boxed{-3}\).
