Using graph paper, solve the following equation. then click on the graph until the correct one is displayed.

y = -| x |

                       /\

                     /    \

                   /        \

                 /            \

               /                \

             /                    \

           /                        \

With vertex at (0,0) and angle of vertex = 90°.

Step-by-step explanation:

|x| is a function whose output depends on whether the input is zero, positive, or negative.  If the input is 0 or positive, the output of the function is x.  If the input is negative, the output of the function is -x.

0 --> 0

5 --> 5

-1 --> 1

-3.14 --> 3.14

-x² --> x²

You can think of absolute value as the magnitude of the number.  -5 and +5 have the same magnitude.  For example, if you walk 5 meters forward and then 5 meters backward, you could say that you walked -5 meters after walking +5 meters, but you still walked 5 meters + 5 meters = 10 meters.  In fact, the total distance you walked is always 0 or greater.  Thus, the absolute value of something tells you its magnitude, which will always be 0 or greater.  In the same way, |x| is always 0 or greater, or |anything| for that matter.

When you put a negative in front of the |x|, you are turning all of the positive magnitudes negative.  Thus, all the outputs of -|x| will be 0 or negative.

0 --> -0

5 --> -5

-1 --> -1

-3.14 --> -3.14

-x² --> -x²

-5 --> -5

1 --> -1

3.14 --> -3.14

x² --> -x²

Notice that when we input the negatives of our first list into -|x|, we get the same negative output as the original numbers.  Generally, when you put -n or n into -|x|, you always get the same number, -n.  Graphically, their y-values will be equal, and you will get a graph that is symmetric across the y-axis.