Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point)
Responses
(1,2)
left parenthesis 1 comma 2 right parenthesis
(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis
(0,−2)
left parenthesis 0 comma negative 2 right parenthesis
(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
To find the point on the graph described by the function, we need to substitute the given values of x and y into the equation and see which option satisfies the equation.
Let's go through each option:
Option 1: (1,2)
Substituting these values into the equation:
y = (2*1 + 1)^2 - 4
y = (2+1)^2 - 4
y = 3^2 - 4
y = 9 - 4
y = 5
So the y-coordinate does not match the equation, therefore (1,2) is not a point on the graph.
Option 2: (-1,-3)
Substituting these values into the equation:
y = (2*-1 + 1)^2 - 4
y = (-2+1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate matches the equation, therefore (-1,-3) is a point on the graph.
Option 3: (0,-2)
Substituting these values into the equation:
y = (2*0 + 1)^2 - 4
y = (0+1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate does not match the equation, therefore (0,-2) is not a point on the graph.
Option 4: (-1,-5)
Substituting these values into the equation:
y = (2*-1 + 1)^2 - 4
y = (-2+1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-coordinate does not match the equation, therefore (-1,-5) is not a point on the graph.
So, the only point on the graph as described by the function is (-1,-3).
To find a point on the graph of the function y=(2x+1)^2-4, we can substitute values for x and solve for y. Let's check each option:
1) If we substitute x = 1 into the function, we get y = (2(1)+1)^2-4 = 3^2-4 = 9-4 = 5. So, the point (1, 5) is NOT on the graph.
2) If we substitute x = -1 into the function, we get y = (2(-1)+1)^2-4 = (-2+1)^2-4 = (-1)^2-4 = 1-4 = -3. So, the point (-1, -3) IS on the graph.
3) If we substitute x = 0 into the function, we get y = (2(0)+1)^2-4 = (0+1)^2-4 = 1^2-4 = 1-4 = -3. So, the point (0, -3) is NOT on the graph.
4) If we substitute x = -1 into the function, we get y = (2(-1)+1)^2-4 = (-2+1)^2-4 = (-1)^2-4 = 1-4 = -3. So, the point (-1, -3) is NOT on the graph.
Therefore, the point on the graph as described by the function y=(2x+1)^2-4 is (-1, -3).
To find the point on the graph described by the function y=(2x+1)2−4, we need to substitute the given coordinate pairs into the equation and see which one satisfies it.
Let's start by checking the first option: (1,2).
To do this, substitute x=1 and y=2 into the equation:
2(1)+1^2−4 = 2+1−4 = -1.
The result is not equal to 2, so (1,2) is not a point on the graph as described by the function.
Now let's check the second option: (−1,−3).
Substituting x=-1 and y=-3:
2(-1)+1^2−4 = -2+1−4 = -5.
The result is equal to -3, so (-1,-3) is a point on the graph.
Now let's check the third option: (0,−2).
Substituting x=0 and y=-2:
2(0)+1^2−4 = 0+1−4 = -3.
The result is not equal to -2, so (0,-2) is not a point on the graph.
Finally, let's check the fourth option: (−1,−5).
Substituting x=-1 and y=-5:
2(-1)+1^2−4 = -2+1−4 = -5.
The result is equal to -5, so (-1,-5) is a point on the graph.
Therefore, the point on the graph as described by the function y=(2x+1)2−4 is (−1,−5).