Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point)
Responses
(0,−2)
left parenthesis 0 comma negative 2 right parenthesis
(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis
(1,2)
left parenthesis 1 comma 2 right parenthesis
(−1,−5)
To find the point on the graph of the function y=(2x+1)²-4, we substitute the x-value into the function and solve for y.
For each of the options given:
(0,−2): plugging in x=0 into the function, we get y=(2(0)+1)²-4 = (1)²-4 = 1-4 = -3, so this point is not on the graph.
(−1,−3): plugging in x=-1 into the function, we get y=(2(-1)+1)²-4 = (-1)²-4 = 1-4 = -3, so this point is not on the graph.
(1,2): plugging in x=1 into the function, we get y=(2(1)+1)²-4 = (2)²-4 = 4-4 = 0, so this point is not on the graph.
(−1,−5): plugging in x=-1 into the function, we get y=(2(-1)+1)²-4 = (-2+1)²-4 = (-1)² - 4 = 1-4 = -3, so this point is on the graph.
Therefore, the correct answer is (−1,−5).