How do you get the vertex of this absolute value?
y = -2 |4x - 1| + 16
By vertex you mean the highest point.
Find out where the expression inside the absolute value is 0. Since the absolute value is always positive, in this expression some quantity is being subtracted from 16. Find the minimum value for that quantity to answer the question.
To find the vertex of the absolute value function, we need to determine the x-coordinate of the vertex.
To do this, we first need to find the x-value where the expression inside the absolute value (4x - 1) is equal to 0.
Set 4x - 1 = 0 and solve for x:
4x - 1 = 0
4x = 1
x = 1/4
Now that we have the x-coordinate of the vertex, we can substitute this value back into the original equation to find the y-coordinate.
Substitute x = 1/4 into the equation:
y = -2 |4(1/4) - 1| + 16
y = -2 |1 - 1| + 16
y = -2(0) + 16
y = 16
Therefore, the vertex of the absolute value function y = -2 |4x - 1| + 16 is (1/4, 16).
The vertex represents the highest or lowest point on the graph of the absolute value function. In this case, it is the highest point since the coefficient of the absolute value is negative (-2).