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

Question

?(1 point)
Responses

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

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

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

(−1,−3)

Answer 1

To determine which of the given points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute the x-values from each point into the equation and check if the computed y-value matches the y-value of the point.

1. Point (1, 2):

   • Substitute \( x = 1 \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] This does not match \( y = 2 \).

2. Point (0, -2):

   • Substitute \( x = 0 \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] This does not match \( y = -2 \).

3. Point (-1, -5):

   • Substitute \( x = -1 \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This does not match \( y = -5 \).

4. Point (-1, -3):

   • Substitute \( x = -1 \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This matches \( y = -3 \).

Thus, the point that lies on the graph of the given function is (-1, -3).