Question

The graph of which inequality has its vertex at (2.5, -5)?

Answer 1

Do they give you any other information?

Answer 2

a. y < |2x - 5| + 5
b. y > |2x + 5| - 5
c. y < |2x + 5| - 5
d. y > |2x - 5| - 5
These are my choices

Answer 3

Did they give you anything else?

Answer 4

The general form of an absolute value equation is y= |mx+h|+k, this being the case, you can use this equation to solve your answer inequalities as if they were equations, because the vertex is a point and it does not matter if it is an inequality or equation when finding the vertex. Look at this example. y=|3x-6|-5. The y value will be the number outside the absolute value symbols, so y=-5. The x value will be when what is inside the absolute value symbols is equal to 0, so 3x-6=0 and solve for x so 3x=6 ->x=6/3=2. This will yield a vertex at (2,-5).

In your case, you are going backwards. Start with the y value, you know it is -5 so it will be an equation with a -5 at the end. Now you need to solve what is inside the absolute value symbols to find which equal 2.5.

Once you have done this, because you are dealing with inequalities, you will need to pick a point inside or outside the inequality, such as (0,0) for outside, or anything above the point (2.5,-5) for inside. Then plug that point into the inequality and see if the inequality is true or false, if it is true then use that one, if it is false use the other.