Answer :
To determine if the point [tex]\((2,0)\)[/tex] lies on the graph of the function [tex]\(v = 2x^2 - x - 6\)[/tex], we need to check if substituting [tex]\(x = 2\)[/tex] into the function yields the corresponding [tex]\(y\)[/tex]-coordinate of 0.
Here are the steps:
1. Substitute [tex]\(x = 2\)[/tex] into the function:
[tex]\[ v = 2(2)^2 - 2 - 6 \][/tex]
2. Calculate [tex]\(2(2)^2\)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
3. Subtract [tex]\(2\)[/tex] from the result:
[tex]\[ 8 - 2 = 6 \][/tex]
4. Subtract [tex]\(6\)[/tex] from the result:
[tex]\[ 6 - 6 = 0 \][/tex]
5. Compare the resulting [tex]\(v\)[/tex] with the [tex]\(y\)[/tex]-coordinate of the point (0):
[tex]\[ v = 0 \quad \text{and} \quad y = 0 \][/tex]
Since the calculated value of [tex]\(v\)[/tex] is equal to the [tex]\(y\)[/tex]-coordinate of the point, the point [tex]\((2,0)\)[/tex] does indeed lie on the graph of the function [tex]\(v = 2x^2 - x - 6\)[/tex].
Therefore, the correct answer is:
A. True
Here are the steps:
1. Substitute [tex]\(x = 2\)[/tex] into the function:
[tex]\[ v = 2(2)^2 - 2 - 6 \][/tex]
2. Calculate [tex]\(2(2)^2\)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
3. Subtract [tex]\(2\)[/tex] from the result:
[tex]\[ 8 - 2 = 6 \][/tex]
4. Subtract [tex]\(6\)[/tex] from the result:
[tex]\[ 6 - 6 = 0 \][/tex]
5. Compare the resulting [tex]\(v\)[/tex] with the [tex]\(y\)[/tex]-coordinate of the point (0):
[tex]\[ v = 0 \quad \text{and} \quad y = 0 \][/tex]
Since the calculated value of [tex]\(v\)[/tex] is equal to the [tex]\(y\)[/tex]-coordinate of the point, the point [tex]\((2,0)\)[/tex] does indeed lie on the graph of the function [tex]\(v = 2x^2 - x - 6\)[/tex].
Therefore, the correct answer is:
A. True
