Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?
(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis
(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
(1,2)
left parenthesis 1 comma 2 right parenthesis
(0,−2)
To find the point on the graph as described by the function y=(2x+1)^2-4, we need to substitute the x-value into the equation and calculate the corresponding y-value.
Let's test each option:
For (−1,−3):
Substituting x=-1 into the equation:
y=(2(-1)+1)^2-4
y=(-2+1)^2-4
y=(-1)^2-4
y=1-4
y=-3
The calculated y-value does not match the given y-value of -3, so (-1,-3) is not a point on the graph as described by the function.
For (−1,−5):
Substituting x=-1 into the equation:
y=(2(-1)+1)^2-4
y=(-2+1)^2-4
y=(-1)^2-4
y=1-4
y=-3
The calculated y-value does not match the given y-value of -5, so (-1,-5) is not a point on the graph as described by the function.
For (1,2):
Substituting x=1 into the equation:
y=(2(1)+1)^2-4
y=(2+1)^2-4
y=3^2-4
y=9-4
y=5
The calculated y-value matches the given y-value of 2, so (1,2) is a point on the graph as described by the function.
For (0,−2):
Substituting x=0 into the equation:
y=(2(0)+1)^2-4
y=(0+1)^2-4
y=1^2-4
y=1-4
y=-3
The calculated y-value does not match the given y-value of -2, so (0,-2) is not a point on the graph as described by the function.
Therefore, the point on the graph as described by the function y=(2x+1)^2-4 is (1,2).
To find a point on the graph of the function y = (2x + 1)^2 - 4, we need to substitute the values of x and calculate the corresponding value of y.
Let's substitute the values from the given options into the equation and see which results in a true statement.
Option 1: (-1, -3)
Substituting x = -1, we have:
y = (2(-1) + 1)^2 - 4
= (-2 + 1)^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
The resulting value of y (-3) matches the given point (-1, -3).
Therefore, the correct answer is (-1, -3).
To find the point on the graph described by the function y=(2x+1)^2-4, we need to substitute the x-coordinate into the equation and solve for the y-coordinate. Let's go through each option:
Option (−1,−3):
Substituting x = -1 into the equation:
y = (2(-1) + 1)^2 - 4
y = (-2 + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The result is y = -3, which matches the given y-coordinate.
Option (−1,−5):
Substituting x = -1 into the equation:
y = (2(-1) + 1)^2 - 4
y = (-2 + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The result is y = -3, not -5. So this option is not correct.
Option (1,2):
Substituting x = 1 into the equation:
y = (2(1) + 1)^2 - 4
y = (2 + 1)^2 - 4
y = (3)^2 - 4
y = 9 - 4
y = 5
The result is y = 5, not 2. So this option is not correct.
Option (0,−2):
Substituting x = 0 into the equation:
y = (2(0) + 1)^2 - 4
y = (0 + 1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
The result is y = -3, not -2. So this option is not correct.
Therefore, the correct point on the graph is (-1, -3).