Problem
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.) Ve this View an example Get more help.
Solution
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 \(\boxed{-3}\).
