which of the following is a point on the graph as described by the function y = (2x + 1)^2 - 4?
(1,2)
(0,-2)
(-1,-3)
(-1,-5)
To find a point on the graph of the function y = (2x + 1)^2 - 4, you need to substitute the x-coordinate into the equation and calculate the corresponding y-coordinate.
Let's check each option:
(1, 2):
When x = 1,
y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5.
Therefore, (1, 2) is not a point on the graph.
(0, -2):
When x = 0,
y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3.
Therefore, (0, -2) is not a point on the graph.
(-1, -3):
When x = -1,
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3.
Therefore, (-1, -3) is a point on the graph.
(-1, -5):
When x = -1,
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3.
Therefore, (-1, -5) is not a point on the graph.
Therefore, the correct point on the graph is (-1, -3).