Question

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

Answer 1

To determine which of the given points lies 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-value matches the y-coordinate of the point.

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

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

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

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

The only point that lies on the graph is \( (-1, -3) \).