What is the vertex of the graph of y=-|3x-12|+5?

Question

anonymous · Answer

The x co-ordinate of the vertex of an absolute value graph will be the value of x which makes the expression within the absolute value signs equal to zero. The y value is what you get when you ignore the absolute value part of the equation.
In this case, the x-value of the vertex is where 3x-12=0, so x=4.
The y value is where y=5.
Do you follow?

anonymous · Answer

I think so

anonymous · Answer

If it makes it more clear to you, the vertex will be where the graphs of:
$$y=-(3x-12)+5$$
and
$$y=3x-12+5$$
cross.
So if we equate them we get:
$$3x-7=-3x+17$$
$$6x=24$$
$$x=4$$
Substituting this into any of the equations will give the corresponding y-value:
$$y=-3((4)-12)+5=5$$