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

Question

𝑦
=
(
2
𝑥
+
1
)
2
−
4
?(1 point)
Responses

(−1,−5)
(
−
1
,
−
5
)
left parenthesis negative 1 comma negative 5 right parenthesis

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

(0,−2)
(
0

Answer 1

To determine which point is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute each \( x \) value from the given points into the equation and see if we obtain the corresponding \( y \) value.

1. For the point \( (-1, -5) \): \[ x = -1 \implies y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \]

   The calculated \( y \) value is \( -3 \), so the point \( (-1, -5) \) is not on the graph.

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

   The calculated \( y \) value is \( -3 \), so the point \( (-1, -3) \) is on the graph.

3. For the point \( (0, -2) \): \[ x = 0 \implies y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = (1)^2 - 4 = 1 - 4 = -3 \]

   The calculated \( y \) value is \( -3 \), so the point \( (0, -2) \) is not on the graph.

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

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