Question

graph this function:
y = 3|x| - 2
click to plot the vertex first.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and a submit button at the bottom)

Explanation:

Step1: Identify the vertex form

The absolute value function is in the form \( y = a|x - h| + k \), where \((h, k)\) is the vertex. For \( y = 3|x| - 2 \), \( h = 0 \) and \( k = -2 \), so the vertex is \((0, -2)\).

Step2: Plot the vertex

On the coordinate plane, find the point where \( x = 0 \) and \( y = -2 \). This is the vertex. Then, to graph the rest of the function, we can use the slope. For \( y = 3|x| - 2 \), when \( x \geq 0 \), the function is \( y = 3x - 2 \) (slope 3), and when \( x < 0 \), it is \( y = -3x - 2 \) (slope -3). We can plot additional points by plugging in \( x \)-values (e.g., \( x = 1 \) gives \( y = 1 \), \( x = -1 \) gives \( y = 1 \)) and drawing the two lines from the vertex with the respective slopes.

Answer:

The vertex of the function \( y = 3|x| - 2 \) is at the point \((0, -2)\). To graph the function, first plot \((0, -2)\), then use the slope of 3 for \( x \geq 0 \) and -3 for \( x < 0 \) to draw the two linear segments forming the V - shape of the absolute value function.