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,−5)left parenthesis negative 1 comma negative 5 right parenthesis(1,2)
To determine if the given points are on the graph of the function y=(2x+1)^2−4, we can plug the x-values of the points into the function and check if the resulting y-values match the y-values of the points.
Let's check each point:
1. (0,−2): Plugging in x=0 into the function:
y = (2*0 + 1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
The result does not match the y-value of the point (0, -2), so this point is not on the graph.
2. (−1,−3): Plugging in 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 result matches the y-value of the point (−1, −3), so this point is on the graph.
3. (−1,−5): Plugging in x=−1 into the function:
We have already calculated this above, and we know that when x=−1, y=−3, not −5. So this point is not on the graph.
4. (1,2): Plugging in 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 result does not match the y-value of the point (1, 2), so this point is not on the graph.
The point that is on the graph of the function y=(2x+1)^2−4 is (−1,−3).