Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?
(−1,−3)
(0,−2)
(−1,−5)
(1,2)
To find the points on the graph described by the function y = (2x + 1)^2 - 4, substitute the given x-values into the equation and calculate the corresponding y-values.
For the points (−1,−3), (0,−2), (−1,−5), and (1,2):
- For (−1,−3):
Substitute x = -1 into the equation: y = (2(-1) + 1)^2 - 4
Simplify: y = ( -2 + 1 )^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
The calculated y-value is -3, which matches the given y-value of -3.
- For (0,−2):
Substitute x = 0 into the equation: y = (2(0) + 1)^2 - 4
Simplify: y = (0 + 1 )^2 - 4
= (1)^2 - 4
= 1 - 4
= -3
The calculated y-value is -3, which does not match the given y-value of -2.
- For (−1,−5):
Substitute x = -1 into the equation: y = (2(-1) + 1)^2 - 4
Simplify: y = (-2 + 1 )^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
The calculated y-value is -3, which does not match the given y-value of -5.
- For (1,2):
Substitute x = 1 into the equation: y = (2(1) + 1)^2 - 4
Simplify: y = (2 + 1 )^2 - 4
= (3)^2 - 4
= 9 - 4
= 5
The calculated y-value is 5, which does not match the given y-value of 2.
Therefore, the only point that lies on the graph described by the function y = (2x + 1)^2 - 4 is (−1,−3).