Question

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

options:

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

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

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

(0,−2)

Answer 1

To determine which points are on the graph of the function \( y = (2x + 1)^2 - 4 \), we can evaluate the function for each of the given \( x \) values and check if the corresponding \( y \) value matches.

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

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

3. For the point \( (-1, -5) \):
We already calculated \( y \) for \( x = -1 \) in the previous step, and it equals \( -3 \), so \( (-1, -5) \) is not on the graph.

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

The only point that is on the graph of the function \( y = (2x + 1)^2 - 4 \) is \( \boxed{(-1, -3)} \).