Which of the following is a point on the graph as described by the function y=(2x+1)^
2−4 ?(1 point) Responses (0,−2) left parenthesis 0 comma negative 2 right parenthesis (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (−1,−3) left parenthesis negative 1 comma negative 3 right parenthesis (1,2)
To find the point on the graph, we need to substitute the x-values into the given function and calculate the corresponding y-values.
Let's calculate the y-values for each option:
For option (0,−2):
- x = 0
- Substitute into the function: y = (2(0)+1)^2 - 4
- Simplify: y = (1)^2 - 4
- Calculate: y = 1 - 4 = -3 (not -2)
For option (−1,−5):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-1)^2 - 4
- Calculate: y = 1 - 4 = -3 (not -5)
For option (−1,−3):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-2+1)^2 - 4
- Calculate: y = (-1)^2 - 4 = 1 - 4 = -3
For option (1,2):
- x = 1
- Substitute into the function: y = (2(1)+1)^2 - 4
- Simplify: y = (2+1)^2 - 4
- Calculate: y = 3^2 - 4 = 9 - 4 = 5
Therefore, the point on the graph as described by the function is (1, 5), which is not one of the given options.
???
Apologies for the confusion. I made an error in my calculations.
Let's go through the options again:
For option (0,−2):
- x = 0
- Substitute into the function: y = (2(0)+1)^2 - 4
- Simplify: y = (1)^2 - 4
- Calculate: y = 1 - 4 = -3 (not -2)
For option (−1,−5):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-2+1)^2 - 4
- Calculate: y = (-1)^2 - 4 = 1 - 4 = -3 (not -5)
For option (−1,−3):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-2+1)^2 - 4
- Calculate: y = (-1)^2 - 4 = 1 - 4 = -3
For option (1,2):
- x = 1
- Substitute into the function: y = (2(1)+1)^2 - 4
- Simplify: y = (2+1)^2 - 4
- Calculate: y = 3^2 - 4 = 9 - 4 = 5
My previous answer was incorrect. The correct point on the graph as described by the function is indeed (1, 5). I apologize for the confusion.
there is no 1,5
Apologies for the confusion. Let's double-check the options:
For option (0,−2):
- x = 0
- Substitute into the function: y = (2(0)+1)^2 - 4
- Simplify: y = (1)^2 - 4
- Calculate: y = 1 - 4 = -3 (not -2)
For option (−1,−5):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-2+1)^2 - 4
- Calculate: y = (-1)^2 - 4 = 1 - 4 = -3
For option (−1,−3):
- x = -1
- Substitute into the function: y = (2(-1)+1)^2 - 4
- Simplify: y = (-2+1)^2 - 4
- Calculate: y = (-1)^2 - 4 = 1 - 4 = -3
For option (1,2):
- x = 1
- Substitute into the function: y = (2(1)+1)^2 - 4
- Simplify: y = (2+1)^2 - 4
- Calculate: y = 3^2 - 4 = 9 - 4 = 5
Apologies for the confusion. You are correct, and I made an error in my previous response. The correct point on the graph as described by the function is (1, 5). Thank you for pointing out the mistake.
To find the point on the graph described by the function y = (2x+1)^2 - 4, we need to substitute the given x-values into the equation and calculate the corresponding y-values. Let's go through each option and evaluate them:
Option 1: (0, -2)
Plugging x = 0 into the equation, we have:
y = (2(0) + 1)^2 - 4
y = (1)^2 - 4
y = 1 - 4
y = -3
Since the y-value is -3, this point does not match the given y-value of -2.
Option 2: (-1, -5)
Using substitution for x = -1:
y = (2(-1) + 1)^2 - 4
y = (-2 + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-value obtained is -3, which does not match the given y-value of -5.
Option 3: (-1, -3)
Substituting x = -1:
y = (2(-1) + 1)^2 - 4
y = (-2 + 1)^2 - 4
y = (-1)^2 - 4
y = 1 - 4
y = -3
The y-value obtained is -3, which matches the given y-value. Therefore, (-1, -3) is the correct point on the graph.
Option 4: (1, 2)
Plugging 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 y-value obtained is 5, which does not match the given y-value of 2.
Therefore, the correct point on the graph as described by the function y = (2x+1)^2 - 4 is (-1, -3).