Question
The function pictured has the form of y=k⋅x2
. What is the value of k
?
graph shows a line passing through (-4,8) (-2,2) (2,2) (4,8)
(1 point)
Responses
0.2
0.2
0
0
2
2
-2
-2
12
. What is the value of k
?
graph shows a line passing through (-4,8) (-2,2) (2,2) (4,8)
(1 point)
Responses
0.2
0.2
0
0
2
2
-2
-2
12
Answers
GPT-4o mini
To find the value of \( k \) in the equation \( y = k \cdot x^2 \), we can use one of the points that the graph passes through. Let’s choose the point \( (2, 2) \).
Substituting \( x = 2 \) and \( y = 2 \) into the equation:
\[
2 = k \cdot (2^2)
\]
This simplifies to:
\[
2 = k \cdot 4
\]
Dividing both sides by 4 gives:
\[
k = \frac{2}{4} = 0.5
\]
Since this is not one of the response options, let's validate with the other points.
Using the point \( (-2, 2) \):
\[
2 = k \cdot (-2)^2
\]
\[
2 = k \cdot 4
\]
\[
k = \frac{2}{4} = 0.5
\]
Using the point \( (-4, 8) \):
\[
8 = k \cdot (-4)^2
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
Using the point \( (4, 8) \):
\[
8 = k \cdot (4)^2
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
It appears that \( k = 0.5 \) meets all conditions but is not listed in the responses. To match the responses, there may be a misinterpretation; \( 0.2 \) is the only value close to half when considered within the options.
However, strictly mathematically, the value we calculated based on the points is \( k = 0.5 \). If the options provided are strictly what you have to choose from, none of them correctly reflect the calculated value based on the points given. Please double-check the problem context for errors in transcription or answer options. In a strict sense of the available options, the best course of action would be to clarify the correct problem formulation.
Substituting \( x = 2 \) and \( y = 2 \) into the equation:
\[
2 = k \cdot (2^2)
\]
This simplifies to:
\[
2 = k \cdot 4
\]
Dividing both sides by 4 gives:
\[
k = \frac{2}{4} = 0.5
\]
Since this is not one of the response options, let's validate with the other points.
Using the point \( (-2, 2) \):
\[
2 = k \cdot (-2)^2
\]
\[
2 = k \cdot 4
\]
\[
k = \frac{2}{4} = 0.5
\]
Using the point \( (-4, 8) \):
\[
8 = k \cdot (-4)^2
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
Using the point \( (4, 8) \):
\[
8 = k \cdot (4)^2
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
It appears that \( k = 0.5 \) meets all conditions but is not listed in the responses. To match the responses, there may be a misinterpretation; \( 0.2 \) is the only value close to half when considered within the options.
However, strictly mathematically, the value we calculated based on the points is \( k = 0.5 \). If the options provided are strictly what you have to choose from, none of them correctly reflect the calculated value based on the points given. Please double-check the problem context for errors in transcription or answer options. In a strict sense of the available options, the best course of action would be to clarify the correct problem formulation.