To find the point on the graph of the function, we need to substitute the x-coordinate into the function and calculate the corresponding y-coordinate.
Let's check each option:
A. (1, 2)
Substituting x=1 into the function:
y=(2(1)+1)^2-4 = 3^2 - 4 = 9 - 4 = 5
However, the y-coordinate is 5, not 2. Therefore, option A is not correct.
B. (-1, -5)
Substituting x=-1 into the function:
y=(2(-1)+1)^2-4 = (-1)^2 - 4 = 1 - 4 = -3
The y-coordinate is -3, not -5. Therefore, option B is not correct.
C. (-1, -3)
Substituting x=-1 into the function:
y=(2(-1)+1)^2-4 = (-2+1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
The y-coordinate is -3, which matches the given option. Therefore, the point (-1, -3) is on the graph.
D. (0,-2)
Substituting x=0 into the function:
y=(2(0)+1)^2-4 = (0+1)^2 - 4 = (1)^2 - 4 = 1 - 4 = -3
The y-coordinate is -3, not -2. Therefore, option D is not correct.
Therefore, the correct answer is C. (-1, -3).
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. (-1, -3)
D.( 0,-2)
1 answer