Which of the following is a point on the graph as described by the function y=(2x+1)^2−4
Responses: (1, 2)
(-1, -3)
(-1, -5)
(0, -2)
To find the point on the graph, we need to substitute the given values of x and y into the equation and see which option satisfies the equation.
Let's substitute (1, 2) into the equation:
y = (2x + 1)^2 - 4
2 = (2(1) + 1)^2 - 4
2 = (2 + 1)^2 - 4
2 = (3)^2 - 4
2 = 9 - 4
2 = 5
The equation does not hold true for (1, 2), so it is not a point on the graph of the given function.
Similarly, let's substitute the values for the other options:
For (-1, -3):
y = (2x + 1)^2 - 4
-3 = (2(-1) + 1)^2 - 4
-3 = (-1)^2 - 4
-3 = 1 - 4
-3 = -3
The equation holds true for (-1, -3), so it is a point on the graph of the given function.
For (-1, -5):
y = (2x + 1)^2 - 4
-5 = (2(-1) + 1)^2 - 4
-5 = (-1)^2 - 4
-5 = 1 - 4
-5 = -3
The equation does not hold true for (-1, -5), so it is not a point on the graph of the given function.
For (0, -2):
y = (2x + 1)^2 - 4
-2 = (2(0) + 1)^2 - 4
-2 = (1)^2 - 4
-2 = 1 - 4
-2 = -3
The equation does not hold true for (0, -2), so it is not a point on the graph of the given function.
Therefore, the only point that satisfies the equation is (-1, -3).