Question

graph this function:
y = |x|
click to plot the vertex first.
(graph with x-axis from -10 to 8, y-axis from -10 to 10, grid lines, and a green submit button below, plus work it out and not feeling ready yet? this can help: text)

Explanation:

Step1: Identify the vertex of \( y = |x| \)

The absolute value function \( y = |x| \) has its vertex at the point where the expression inside the absolute value is zero. For \( y = |x| \), when \( x = 0 \), \( y = |0| = 0 \). So the vertex is at \( (0, 0) \).

Step2: Find other points to plot

• For \( x = 1 \), \( y = |1| = 1 \), so the point is \( (1, 1) \).
• For \( x = -1 \), \( y = | - 1| = 1 \), so the point is \( (-1, 1) \).
• For \( x = 2 \), \( y = |2| = 2 \), so the point is \( (2, 2) \).
• For \( x = -2 \), \( y = | - 2| = 2 \), so the point is \( (-2, 2) \).

Plot the vertex \( (0, 0) \) first, then plot the other points. The graph of \( y = |x| \) is a V - shaped graph opening upwards with the vertex at the origin and passing through the points we found.

Answer:

The vertex of the function \( y = |x| \) is at \( (0, 0) \), and the graph is a V - shaped graph opening upwards with points like \( (1, 1) \), \( (-1, 1) \), \( (2, 2) \), \( (-2, 2) \) etc. plotted. (To graph, first plot \( (0, 0) \), then plot the other points and draw the two rays of the V - shape.)