Which of the following is a point on the graph as described by the function y= (2x + 1) ^ 2 -4? (1 point)
O (1, 2)
O (- 1, - 5)
O (0, - 2)
(- 1, - 3)
To find the point(s) on the graph, we need to substitute the given values of x and find the corresponding value of y.
a) For (1, 2):
y = (2(1) + 1)^2 - 4
= (2 + 1)^2 - 4
= 3^2 - 4
= 9 - 4
= 5
Therefore, this point does not satisfy the equation y = (2x + 1)^2 - 4, so (1, 2) is not a point on the graph.
b) For (-1, -5):
y = (2(-1) + 1)^2 - 4
= (-2 + 1)^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
Therefore, this point does not satisfy the equation y = (2x + 1)^2 - 4, so (-1, -5) is not a point on the graph.
c) For (0, -2):
y = (2(0) + 1)^2 - 4
= (0 + 1)^2 - 4
= 1^2 - 4
= 1 - 4
= -3
Therefore, this point does not satisfy the equation y = (2x + 1)^2 - 4, so (0, -2) is not a point on the graph.
d) For (-1, -3):
y = (2(-1) + 1)^2 - 4
= (-2 + 1)^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
Therefore, this point satisfies the equation y = (2x + 1)^2 - 4, so (-1, -3) is a point on the graph.
The correct answer is: (-1, -3)