Which of the following is a point on the graph as described by the function y=(2x+1)2-4?
(1,2)
(-1,-5)
(0,-2)
(-1,-3)
To find the point on the graph, we substitute the x-coordinate into the function and evaluate it to find the corresponding y-coordinate.
1. For point (1,2):
Substituting x=1 into the function:
y = (2(1) + 1)^2 - 4
y = (2+1)^2 - 4
y = 3^2 - 4
y = 9 - 4
y = 5
The y-coordinate is 5.
2. For point (-1, -5):
Substituting x=-1 into the function:
y = (2(-1) + 1)^2 - 4
y = (-2+1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate is -3.
3. For point (0, -2):
Substituting x=0 into the function:
y = (2(0) + 1)^2 - 4
y = (0+1)^2 - 4
y = 1^2 - 4
y = 1 - 4
y = -3
The y-coordinate is -3.
4. For point (-1, -3):
Substituting x=-1 into the function:
y = (2(-1) + 1)^2 - 4
y = (-2+1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate is -3.
From the given points, only (1,2) is not a point on the graph described by the function y=(2x+1)2-4.