Question

graph this function:
$y = |-2x| + 4$
click to plot the vertex first.

Explanation:

Step1: Recall absolute value function form

The general form of an absolute value function is \( y = a|x - h| + k \), where \((h, k)\) is the vertex. For the function \( y = |-2x| + 4 \), we can simplify \( |-2x| \) to \( 2|x| \) (since \( |-2x| = |-2||x| = 2|x| \)), so the function becomes \( y = 2|x| + 4 \). In the form \( y = a|x - h| + k \), \( h = 0 \) and \( k = 4 \).

Step2: Determine the vertex

From the form, the vertex \((h, k)\) is \((0, 4)\). So we plot the vertex at the point \((0, 4)\) on the coordinate plane. Then, to graph the rest of the function, we can use the slope. For \( y = 2|x| + 4 \), when \( x \geq 0 \), the function is \( y = 2x + 4 \) (slope \( 2 \)), and when \( x < 0 \), the function is \( y = -2x + 4 \) (slope \( -2 \)). We can plot additional points using these slopes (e.g., for \( x = 1 \), \( y = 6 \); for \( x = -1 \), \( y = 6 \)) and draw the two rays of the absolute value graph from the vertex.

Answer:

The vertex of the function \( y = |-2x| + 4 \) is at the point \((0, 4)\), so we plot the vertex at \((0, 4)\) first, then use the slope to plot other points and draw the graph.