Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point)Responses(−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 which point is on the graph of the function y=(2x+1)²−4, we need to substitute the x-coordinate of each point into the function and see if the resulting y-coordinate matches.
Let's check each point:
1) Substituting x = -1 into the function:
y = (2(-1)+1)² - 4
y = (2-1)² - 4
y = 1² - 4
y = 1 - 4
y = -3
So, the point (−1,−3) is on the graph.
2) Substituting x = -1 into the function:
y = (2(-1)+1)² - 4
y = (2-1)² - 4
y = 1² - 4
y = 1 - 4
y = -3
So, the point (−1,−3) is on the graph.
3) Substituting x = 1 into the function:
y = (2(1)+1)² - 4
y = (2+1)² - 4
y = 3² - 4
y = 9 - 4
y = 5
So, the point (1,2) is on the graph.
4) Substituting x = 0 into the function:
y = (2(0)+1)² - 4
y = (0+1)² - 4
y = 1² - 4
y = 1 - 4
y = -3
So, the point (0,-2) is not on the graph.
Therefore, the correct answer is (−1,−3).
are you sure
Apologies for the error in my previous response. Let's check the points again:
1) Substituting x = -1 into the function:
y = (2(-1)+1)² - 4
y = ( -2 + 1)² - 4
y = (-1)² - 4
y = 1 - 4
y = -3
So, the point (-1,-3) is on the graph.
2) Substituting x = -1 into the function:
y = (2(-1)+1)² - 4
y = ( -2 + 1)² - 4
y = (-1)² - 4
y = 1 - 4
y = -3
So, the point (-1,-3) is on the graph.
3) Substituting x = 1 into the function:
y = (2(1)+1)² - 4
y = (2 + 1)² - 4
y = 3² - 4
y = 9 - 4
y = 5
So, the point (1,5) is not on the graph.
4) Substituting x = 0 into the function:
y = (2(0)+1)² - 4
y = (0 + 1)² - 4
y = 1² - 4
y = 1 - 4
y = -3
So, the point (0,-3) is on the graph.
Therefore, the correct answer is (-1,-3). Apologies for the confusion in my previous response.
To determine which point on the graph of the function y = (2x + 1)^2 - 4 corresponds to the given options, we can substitute the x and y values of each option into the equation and see which one satisfies it.
Let's calculate the y-values for each option:
1. For option (−1, −3):
Substitute 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 (-3) matches the given y-value (-3) from the option. So, option (−1,−3) is a point on the graph.
2. For option (−1, −5):
Substitute 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 (-3) does not match the given y-value (-5). So, option (−1,−5) is not a point on the graph.
3. For option (1, 2):
Substitute 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 (5) does not match the given y-value (2). So, option (1,2) is not a point on the graph.
4. For option (0,−2):
Substitute 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 (-3) does not match the given y-value (-2). So, option (0,−2) is not a point on the graph.
Therefore, the point on the graph described by the function y = (2x + 1)^2 - 4 is (−1,−3).