Question

Graph with step by step y=-3|x+1|+2

Answer 1

To graph the equation y = -3|x + 1| + 2, we start by identifying key points on the graph and then plot them to create the graph.

Step-by-step explanation:

To graph the equation y = -3|x + 1| + 2, we will start by identifying the key points on the graph.

1. When x = -1, the absolute value term becomes 0 and y = -3(0) + 2 = 2. So the point (-1, 2) is on the graph.
2. When x < -1, the expression inside the absolute value term is negative. So for x = -2, -3, -4, we have y = -3(-2 + 1) + 2 = 7, y = -3(-3 + 1) + 2 = 11, and y = -3(-4 + 1) + 2 = 14. So the points (-2, 7), (-3, 11), and (-4, 14) are on the graph.
3. When x > -1, the expression inside the absolute value term is positive. So for x = 0, 1, 2, we have y = -3(0 + 1) + 2 = -1, y = -3(1 + 1) + 2 = -1, and y = -3(2 + 1) + 2 = -7. So the points (0, -1), (1, -1), and (2, -7) are on the graph.

Plotting these points on the xy-plane and connecting them with a smooth curve will give us the graph of y = -3|x + 1| + 2.