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 determine if a point is on the graph of a function, we can substitute the x-coordinate of the point into the equation and see if it satisfies the equation.
Let's test each of the given points:
1. (-1, -3)
y = (2(-1)+1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
The y-coordinate from the equation doesn't match the given y-coordinate of -3, so (-1, -3) is not a point on the graph.
2. (0, -2)
y = (2(0)+1)^2 - 4 = (0+1)^2 - 4 = 1 - 4 = -3
The y-coordinate from the equation doesn't match the given y-coordinate of -2, so (0, -2) is not a point on the graph.
3. (-1, -5)
y = (2(-1)+1)^2 - 4 = (-2+1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3
The y-coordinate from the equation doesn't match the given y-coordinate of -5, so (-1, -5) is not a point on the graph.
4. (1, 2)
y = (2(1)+1)^2 - 4 = (2+1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5
The y-coordinate from the equation does match the given y-coordinate of 2, so (1, 2) is a point on the graph.
Therefore, the correct answer is (1, 2).