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

Question

?(1 point)
Responses

(0,−2)
left parenthesis 0 comma negative 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

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

Answer 1

To find which of the given points is on the graph described by the function \( y = (2x + 1)^2 - 4 \), we need to substitute the \( x \)-values of each point into the function and see if we get the corresponding \( y \)-value.

Let's evaluate each option one by one.

1. Point (0, -2): \[ y = (2(0) + 1)^2 - 4 = (1)^2 - 4 = 1 - 4 = -3 \] The result is \( -3 \), so (0, -2) is not a point on the graph.

2. Point (-1, -3): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] The result is \( -3 \), so (-1, -3) is a point on the graph.

3. Point (-1, -5): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] The result is \( -3 \), so (-1, -5) is not a point on the graph.

4. Point (1, 2): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = (3)^2 - 4 = 9 - 4 = 5 \] The result is \( 5 \), so (1, 2) is not a point on the graph.

After evaluating all the options, the correct point on the graph is: \[ \boxed{(-1, -3)} \]