Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ? (1 point) Responses A. (0,−2) B. (1,2) C. (−1,−3) D. (−1,−5)
To find a point on the graph of the function y=(2x+1)2−4, we need to substitute values of x into the function and solve for y.
A. (0,−2): y=(2(0)+1)2−4 = 1-4 = -3
The y-coordinate does not match, so (0,−2) is not a point on the graph.
B. (1,2): y=(2(1)+1)2−4 = 3^2-4 = 9-4 = 5
The y-coordinate does not match, so (1,2) is not a point on the graph.
C. (−1,−3): y=(2(-1)+1)2−4 = (-2+1)2-4 = (-1)2-4 = 1-4 = -3
The coordinates match, so (−1,−3) is a point on the graph.
D. (−1,−5): y=(2(-1)+1)2−4 = (-2+1)2-4 = (-1)2-4 = 1-4 = -3
The y-coordinate does not match, so (−1,−5) is not a point on the graph.
The correct answer is C. (−1,−3)