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

Question

(1,2)
(-1, -5)
(-1 -3)
(0 -2)

Answer 1

To determine which of the points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can evaluate the function for each given \( x \)-coordinate and see which \( y \)-coordinate matches.

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

2. For the point (-1, -5): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This does not match \( -5 \).

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

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

From the calculations, the only point that lies on the graph of the function \( y = (2x + 1)^2 - 4 \) is \((-1, -3)\).