Question
The function pictured has the form of y=k(x2). What is the value of k?
graph shows a line passing through (-4,4) (-2,1) (2,1) (4,4) and (0,0)
(1 point)
Responses
2
2
1
1
14
1 fourth
12
graph shows a line passing through (-4,4) (-2,1) (2,1) (4,4) and (0,0)
(1 point)
Responses
2
2
1
1
14
1 fourth
12
Answers
GPT-4o mini
The function you described has the form \( y = k(x^2) \).
To find the value of \( k \), we can use one of the points that the graph passes through. We'll use the point (2, 1):
1. Substituting \( x = 2 \) and \( y = 1 \) into the equation \( y = k(x^2) \):
\[
1 = k(2^2)
\]
2. This simplifies to:
\[
1 = k \cdot 4
\]
3. To solve for \( k \), we divide both sides by 4:
\[
k = \frac{1}{4}
\]
Therefore, the value of \( k \) is \( \frac{1}{4} \).
To find the value of \( k \), we can use one of the points that the graph passes through. We'll use the point (2, 1):
1. Substituting \( x = 2 \) and \( y = 1 \) into the equation \( y = k(x^2) \):
\[
1 = k(2^2)
\]
2. This simplifies to:
\[
1 = k \cdot 4
\]
3. To solve for \( k \), we divide both sides by 4:
\[
k = \frac{1}{4}
\]
Therefore, the value of \( k \) is \( \frac{1}{4} \).