Question

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

(1,2)
(0,−2)
(−1,−5)
(−1,−3)

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

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 function and check if the resulting y-value matches the one given in the point.

Let's test each point:

1. For the point (1,2):
Substitute x = 1 into the function:
y = (2(1)+1)² − 4
y = (2+1)² − 4
y = (3)² − 4
y = 9 − 4
y = 5
Since 5 does not match the y-value of 2, the point (1,2) is not on the graph.

2. For the point (0,−2):
Substitute x = 0 into the function:
y = (2(0)+1)² − 4
y = (1)² − 4
y = 1 − 4
y = −3
Since −3 does not match the y-value of -2, the point (0,−2) is not on the graph.

3. For the point (−1,−5):
Substitute x = -1 into the function:
y = (2(−1)+1)² − 4
y = (−2+1)² − 4
y = (−1)² − 4
y = 1 − 4
y = −3
Since −3 does not match the y-value of -5, the point (−1,−5) is not on the graph.

4. For the point (−1,−3):
Substitute x = -1 into the function:
y = (2(−1)+1)² − 4
y = (−2+1)² − 4
y = (−1)² − 4
y = 1 − 4
y = −3
Since −3 matches the y-value given in the point (−1,−3), this point is on the graph.

Therefore, the point that is on the graph of the function y = (2x+1)² − 4 is (−1,−3).