Which of the following is a point on the graph as described by the function y= (2x+1) to the power of 2 -4?
(-1,3)
(1,2)
(0,-2)
(-1,-5)
To determine if a point is on the graph as described by the function y = (2x+1)^2 - 4, we substitute the x-coordinate of the point into the equation and check if it satisfies the equation's relationship.
1) For (-1,3):
y = (2(-1) + 1)^2 - 4 -> y = (-1)^2 - 4 -> y = 1 - 4 -> y = -3
The y-coordinate (-3) does not match the y-value of the function (3).
2) 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 (5) does not match the y-value of the function (2).
3) For (0,-2):
y = (2(0) + 1)^2 - 4 -> y = (0 + 1)^2 - 4 -> y = 1^2 - 4 -> y = 1 - 4 -> y = -3
The y-coordinate (-3) does not match the y-value of the function (-2).
4) 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 (-3) does match the y-value of the function (-5).
Thus, the only point that is on the graph as described by the function y = (2x+1)^2 - 4 is (-1,-5).