Questions: What is the vertex of the function f(x)=-1/2x+8-5 ? (-8,-5) (-8,5) (8,5) (8,-5)

Solution Steps

To find the vertex of the function \( f(x) = -\frac{1}{2}|x+8| - 5 \), we need to identify the point where the expression inside the absolute value is zero, and then apply the transformations given by the function.

1. The expression inside the absolute value is zero when \( x + 8 = 0 \), so \( x = -8 \).
2. The function \( f(x) = -\frac{1}{2}|x+8| - 5 \) translates the graph of \( -\frac{1}{2}|x| \) horizontally by -8 units and vertically by -5 units.
3. Therefore, the vertex of the function is at the point \((-8, -5)\).

To find the vertex of the function \( f(x) = -\frac{1}{2}|x+8| - 5 \), we first determine where the expression inside the absolute value equals zero. This occurs when:

\[ x + 8 = 0 \implies x = -8 \]

Next, we substitute \( x = -8 \) into the function to find the corresponding \( y \)-coordinate of the vertex:

\[ f(-8) = -\frac{1}{2}|-8 + 8| - 5 = -\frac{1}{2}|0| - 5 = -5 \]

Thus, the vertex of the function is at the point:

\[ (-8, -5) \]

Final Answer