Question

graph this function:
y = -|x|
click to plot the vertex first.

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.