Question

what is a point on a graph described by this function y = (2x + 1)^2 - 4?

(-1, -5)
(1, 2)
(0, -2)
(-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 plug in the x-coordinates of the points into the function and see if the resulting y-value matches the y-coordinate of the point.

1. **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 with -5.

2. **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 with 2.

3. **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 with -2.

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

The point on the graph described by the function is **(-1, -3)**.