which of the following is a point on the graph as described by the function y=(2x+1)^2-4?
a. (1,2)
b. (-1,-5)
c. (0,-2)
d. (-1, -3)
To find the point on the graph as described by the function, we need to substitute the x-coordinate into the function to find the corresponding y-coordinate.
a. (1,2):
Substituting x = 1 into the function, we get y = (2(1)+1)^2-4 = 3^2-4 = 5.
So, (1,2) is not a point on the graph.
b. (-1,-5):
Substituting x = -1 into the function, we get y = (2(-1)+1)^2-4 = (-2+1)^2-4 = (-1)^2-4 = 1-4 = -3.
So, (-1,-5) is not a point on the graph.
c. (0,-2):
Substituting x = 0 into the function, we get y = (2(0)+1)^2-4 = (0+1)^2-4 = 1^2-4 = 1-4 = -3.
So, (0,-2) is not a point on the graph.
d. (-1, -3):
Substituting x = -1 into the function, we get y = (2(-1)+1)^2-4 = (-2+1)^2-4 = (-1)^2-4 = 1-4 = -3.
So, (-1, -3) is a point on the graph.
The correct answer is d. (-1, -3).