Question

Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point) Responses (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (−1,−3) left parenthesis negative 1 comma negative 3 right parenthesis (0,−2)

Answer 1

To determine which points are on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute the x-coordinates of each point into the function and see if we get the corresponding y-coordinates.

1. For the point \((-1, -5)\):
\[
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
\]
The point is \((-1, -3)\), not \((-1, -5)\).

2. For the point \((1, 2)\):
\[
y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5
\]
The point is \((1, 5)\), not \((1, 2)\).

3. For the point \((-1, -3)\):
\[
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
\]
This point \((-1, -3)\) is on the graph.

4. For the point \((0, -2)\):
\[
y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3
\]
The point is \((0, -3)\), not \((0, -2)\).

Thus, the point on the graph is:

\((-1, -3)\).