Which of the following is a point on the graph as described by the function y=(2x+1)2−4?
(0,−2)
(−1,−3)
(−1,−5)
(1,2)
Let's plug in the x-coordinate of each point into the given function and see if they match the y-coordinate.
For (0, -2):
y = (2(0) + 1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate does not match, so (0, -2) is not a point on the graph.
For (-1, -3):
y = (2(-1) + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate matches, so (-1, -3) is a point on the graph.
For (-1, -5):
y = (2(-1) + 1)^2 - 4
y = (-2 + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate does not match, so (-1, -5) is not a point on the graph.
For (1, 2):
y = (2(1) + 1)^2 - 4
y = (2 + 1)^2 - 4
y = (3)^2 - 4
y = 9 - 4
y = 5
The y-coordinate does not match, so (1, 2) is not a point on the graph.
Therefore, the only point on the graph is (-1, -3).