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

Question

?(1 point)
Responses

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

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

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

(1,2)

Answer 1

To determine which of the given points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can plug in the x-coordinates of the points into the function and see if the y-coordinates match.

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

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

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

3. For \( x = -1 \): (Already calculated) The point \( (-1, -5) \) is NOT on the graph.

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

The only point that lies on the graph is:

\((−1,−3)\)