graph this function:\n y = -|x|\nclick to plot the vertex first.

Answer

Explanation:

Step1: Find the vertex of ( y = -|x| )

The absolute - value function ( y = |x| ) has a vertex at ( (0,0) ). For the function ( y=-|x| ), the transformation (a reflection over the x - axis) does not change the x - coordinate of the vertex. So, we substitute ( x = 0 ) into ( y=-|x| ), we get ( y=-|0| = 0 ). So the vertex of ( y=-|x| ) is at the point ( (0,0) ).

Step2: Find other points to graph the function

We can choose some values of ( x ) and find the corresponding ( y ) values.

When ( x = 1 ), ( y=-|1|=- 1 ), so the point is ( (1, - 1) ).
When ( x=-1 ), ( y=-|-1|=-1 ), so the point is ( (-1, - 1) ).
When ( x = 2 ), ( y=-|2|=-2 ), so the point is ( (2, - 2) ).
When ( x=-2 ), ( y=-|-2|=-2 ), so the point is ( (-2, - 2) ).

To graph the function, first plot the vertex ( (0,0) ). Then, using the other points we found (such as ( (1, - 1) ), ( (-1, - 1) ), ( (2, - 2) ), ( (-2, - 2) )), we can see that the graph of ( y = -|x| ) is a "V - shaped" graph opening downward with the vertex at the origin and passing through the other points we calculated.

Answer:

The vertex of the function ( y=-|x| ) is at ( (0,0) ). To graph the function, plot the vertex ( (0,0) ) first, and then plot other points like ( (1, - 1) ), ( (-1, - 1) ), ( (2, - 2) ), ( (-2, - 2) ) and draw a "V - shaped" graph opening downward.