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) left parenthesis negative 1 comma negative 5 right parenthesis
To find the point on the graph as described by the function, we need to substitute the x-coordinate into the function and solve for y.
For option (0,−2), let's substitute x = 0 into the function:
y = (2(0) + 1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
So, (0,−2) is not a point on the graph as described by the function.
For option (−1,−3), let's substitute 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
So, (−1,−3) is a point on the graph as described by the function.
For option (1,2), let's substitute 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
So, (1,2) is a point on the graph as described by the function.
For option (−1,−5), let's substitute 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
So, (−1,−5) is not a point on the graph as described by the function.
Therefore, the correct point on the graph as described by the function is (−1,−3) or option (−1,−3).