Question

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

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

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

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

(1,2)
(
1
,
2
)

Answer 1

To determine which of the given points lies on the graph of the function \( y = (2x + 1)^2 - 4 \), we will evaluate the function for each x-coordinate in the options provided and see if the resulting y-coordinate matches any of the given points.

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

2. **For \( x = 0 \)**:
\[
y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3
\]
So the point \((0, -2)\) is NOT on the graph.

3. **For \( x = -1 \)** (already calculated):
We already computed this and found that \( y = -3 \), confirming that \((-1, -3)\) is on the graph.

4. **For \( x = 1 \)**:
\[
y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5
\]
So the point \((1, 2)\) is NOT on the graph.

After evaluating all options, we find that the only point that matches is \((-1, -3)\).

**Answer:** \((-1, -3)\)