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

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis
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Answer 1

To determine which of the given points lies on the graph described by the function \( y = (2x + 1)^2 - 4 \), we need to substitute the x-coordinates of each point into the function and see if the resulting y-value matches the y-coordinate of the point.

Let's evaluate the function for each x-coordinate from the choices provided:

1. **For the point \((-1, -5)\)**:
\[
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
\]
The point \((-1, -5)\) does not lie on the graph.

2. **For the point \((0, -2)\)**:
\[
y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3
\]
The point \((0, -2)\) does not lie on the graph.

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

4. **For the point \((-1, -3)\)**:
\[
y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
\]
The point \((-1, -3)\) does lie on the graph.

Thus, the correct point on the graph is \((-1, -3)\).