Which of the following is a point on the graph as described by the function y=(2x+1)^2-4? A. (-1,-5) b. (-1,-3) c. 1,2 d. 0,-2
To find a point on the graph of the given function, we need to substitute a value of x into the function and solve for y.
a) (-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 point (-1,-5) is not on the graph of the function.
b) (-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 point (-1,-3) is on the graph of the function.
c) (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 point (1,2) is not on the graph of the function.
d) (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 point (0,-2) is not on the graph of the function.
Therefore, the correct answer is b) (-1,-3).