Question

question
use technology to find points and then graph the function $y = 2|x| + 4$, following the instructions below.
plot at least five points that fit on the axes below. click a point to delete it.
watch video show example

Explanation:

Step1: Choose x-values

Select x-values: -2, -1, 0, 1, 2.

Step2: Calculate y for x=-2

Substitute x=-2 into \( y = 2|x| + 4 \): \( y = 2|-2| + 4 = 2(2) + 4 = 8 \). Point: (-2, 8)

Step3: Calculate y for x=-1

Substitute x=-1: \( y = 2|-1| + 4 = 2(1) + 4 = 6 \). Point: (-1, 6)

Step4: Calculate y for x=0

Substitute x=0: \( y = 2|0| + 4 = 0 + 4 = 4 \). Point: (0, 4)

Step5: Calculate y for x=1

Substitute x=1: \( y = 2|1| + 4 = 2(1) + 4 = 6 \). Point: (1, 6)

Step6: Calculate y for x=2

Substitute x=2: \( y = 2|2| + 4 = 2(2) + 4 = 8 \). Point: (2, 8)

Step7: Graph the points

Plot (-2, 8), (-1, 6), (0, 4), (1, 6), (2, 8). The graph is a V - shaped graph (absolute value graph) opening upwards, with vertex at (0, 4), and steeper than \( y = |x| \) due to the coefficient 2.

Answer:

Points: (-2, 8), (-1, 6), (0, 4), (1, 6), (2, 8). The graph is a V - shaped graph with vertex at (0, 4), passing through the calculated points.