Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point) Responses (−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 (0,−2)

Answer 1

To find out which of the provided points lie on the graph of the function \(y = (2x + 1)^2 - 4\), we can substitute the x-coordinate of each point into the function and check if the resulting y-coordinate matches the one given in the point.

Let's check each point one by one:

1. (-1, -3): For this point, \(x = -1\).
\[y = (2(-1) + 1)^2 - 4\]
\[y = (-2 + 1)^2 - 4\]
\[y = (-1)^2 - 4\]
\[y = 1 - 4\]
\[y = -3\]
Since we got \(y = -3\), the point (-1, -3) does lie on the graph of the function.

2. (1, 2): For this point, \(x = 1\).
\[y = (2(1) + 1)^2 - 4\]
\[y = (2 + 1)^2 - 4\]
\[y = (3)^2 - 4\]
\[y = 9 - 4\]
\[y = 5\]
Since we got \(y = 5\), the point (1, 2) does not lie on the graph of the function.

3. (-1, -5): This is already incorrect because we found for point (-1, -3) that the correct y value for \(x = -1\) is \(-3\), not \(-5\).

4. (0, -2): For this point, \(x = 0\).
\[y = (2(0) + 1)^2 - 4\]
\[y = (0 + 1)^2 - 4\]
\[y = (1)^2 - 4\]
\[y = 1 - 4\]
\[y = -3\]
Since we got \(y = -3\), the point (0, -2) does not lie on the graph of the function.

Therefore, the only point from the given options that lies on the graph of the function \(y = (2x + 1)^2 - 4\) is (-1, -3).