Final answer:
The slope of the absolute value function is -6 and the vertex is (-3, 7).
Step-by-step explanation:
The given function is y = -6|x+3|+7.
The slope of the absolute value function depends on whether the expression inside the absolute value is positive or negative. In this case, the expression is x+3.
When x+3 is positive, the function simplifies to y = -6(x+3)+7. So the slope is -6.
When x+3 is negative, the function simplifies to y = -6(-(x+3))+7. So the slope is also -6.
The vertex of the absolute value function is the point where the graph reaches its minimum or maximum value. In this case, the vertex occurs when the expression inside the absolute value equals zero. So x+3 = 0, which means x = -3.
Substituting x = -3 into the function, we get y = -6|-3+3|+7 = -6|0|+7 = -6(0)+7 = 7.
Therefore, the slope of the absolute value function is -6 and the vertex is (-3, 7).