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)
and curves and passes through (0,0)
(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)
and curves and passes through (0,0)
(1 point)
Responses
0.2
0.2
0
0
2
2
-2
-2
12
Answers
GPT-4o mini
To determine the value of \( k \) in the equation \( y = k \cdot x^2 \), we can use one of the points on the graph. The point (0, 0) confirms that the function passes through the origin, which is expected for this quadratic function. However, we can also use the other points to find \( k \).
Let's use the point (-2, 2) for this calculation:
1. Substitute \( x = -2 \) and \( y = 2 \) into the equation:
\[
2 = k \cdot (-2)^2
\]
This simplifies to:
\[
2 = k \cdot 4
\]
2. Now, solve for \( k \):
\[
k = \frac{2}{4} = 0.5
\]
Let's check with another point, say (2, 2):
1. Substitute \( x = 2 \) and \( y = 2 \):
\[
2 = k \cdot (2)^2
\]
This simplifies to:
\[
2 = k \cdot 4
\]
2. Solve for \( k \):
\[
k = \frac{2}{4} = 0.5
\]
Finally, we can double-check with the points (-4, 8) or (4, 8):
1. Using (4, 8):
\[
8 = k \cdot (4)^2
\]
This simplifies to:
\[
8 = k \cdot 16
\]
2. Solve for \( k \):
\[
k = \frac{8}{16} = 0.5
\]
It appears that there is a mismatch between the calculated value and the provided responses. However, based on the calculations using the points, we determined that the value of \( k \) is \( 0.5 \), but it is not listed among the response options (0.2, 0, 2, -2, 12).
If there’s still room for troubleshooting, indicating a different equation form or providing additional context on the graph may yield more accurate results.
Let's use the point (-2, 2) for this calculation:
1. Substitute \( x = -2 \) and \( y = 2 \) into the equation:
\[
2 = k \cdot (-2)^2
\]
This simplifies to:
\[
2 = k \cdot 4
\]
2. Now, solve for \( k \):
\[
k = \frac{2}{4} = 0.5
\]
Let's check with another point, say (2, 2):
1. Substitute \( x = 2 \) and \( y = 2 \):
\[
2 = k \cdot (2)^2
\]
This simplifies to:
\[
2 = k \cdot 4
\]
2. Solve for \( k \):
\[
k = \frac{2}{4} = 0.5
\]
Finally, we can double-check with the points (-4, 8) or (4, 8):
1. Using (4, 8):
\[
8 = k \cdot (4)^2
\]
This simplifies to:
\[
8 = k \cdot 16
\]
2. Solve for \( k \):
\[
k = \frac{8}{16} = 0.5
\]
It appears that there is a mismatch between the calculated value and the provided responses. However, based on the calculations using the points, we determined that the value of \( k \) is \( 0.5 \), but it is not listed among the response options (0.2, 0, 2, -2, 12).
If there’s still room for troubleshooting, indicating a different equation form or providing additional context on the graph may yield more accurate results.