Question

use technology to find points and then graph the function $y = -(x - 2)^2 + 2$, following the instructions below.

done plotting points

plot at least five points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x-values

Let's choose x-values: 0, 1, 2, 3, 4.

Step2: Calculate y for x=0

Substitute x=0 into \( y = -(x - 2)^2 + 2 \):
\( y = -(0 - 2)^2 + 2 = -4 + 2 = -2 \). So point (0, -2).

Step3: Calculate y for x=1

Substitute x=1:
\( y = -(1 - 2)^2 + 2 = -1 + 2 = 1 \). So point (1, 1).

Step4: Calculate y for x=2

Substitute x=2:
\( y = -(2 - 2)^2 + 2 = 0 + 2 = 2 \). So point (2, 2).

Step5: Calculate y for x=3

Substitute x=3:
\( y = -(3 - 2)^2 + 2 = -1 + 2 = 1 \). So point (3, 1).

Step6: Calculate y for x=4

Substitute x=4:
\( y = -(4 - 2)^2 + 2 = -4 + 2 = -2 \). So point (4, -2).

Answer:

Five points are (0, -2), (1, 1), (2, 2), (3, 1), (4, -2). Plot these on the graph.