Question
The function pictured has the form of y=k⋅x2y=k⋅x2 . What is the value of kk ? (1 point) Responses 0 0 2 2 -2 -2 12121 half 0.2
Graph:
(-4,8)
(-2,2)
(0,0)
(2,2)
(4,8)
Graph:
(-4,8)
(-2,2)
(0,0)
(2,2)
(4,8)
Answers
GPT-4o mini
To find the value of \( k \) in the function \( y = k \cdot x^2 \), we need to use one of the points provided in the graph.
From the point \((2, 2)\), we substitute \( x = 2 \) and \( y = 2 \):
\[
2 = k \cdot (2^2)
\]
This simplifies to:
\[
2 = k \cdot 4
\]
To solve for \( k \), we divide both sides by \( 4 \):
\[
k = \frac{2}{4} = 0.5
\]
Converting \( 0.5 \) into a fraction gives us \( \frac{1}{2} \) or \( 0.2 \) if scaled appropriately for the options. However, it's still seen as part of a standard answer; commonly one would retain \( k = 0.5 \) rather than giving the fraction.
Let's verify this with another point, say \((4, 8)\):
Substituting \( x = 4 \) and \( y = 8\):
\[
8 = k \cdot (4^2)
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
Both calculations confirm:
Thus, the value of \( k \) is \( \textbf{half} \) or \( 0.5 \).
From the point \((2, 2)\), we substitute \( x = 2 \) and \( y = 2 \):
\[
2 = k \cdot (2^2)
\]
This simplifies to:
\[
2 = k \cdot 4
\]
To solve for \( k \), we divide both sides by \( 4 \):
\[
k = \frac{2}{4} = 0.5
\]
Converting \( 0.5 \) into a fraction gives us \( \frac{1}{2} \) or \( 0.2 \) if scaled appropriately for the options. However, it's still seen as part of a standard answer; commonly one would retain \( k = 0.5 \) rather than giving the fraction.
Let's verify this with another point, say \((4, 8)\):
Substituting \( x = 4 \) and \( y = 8\):
\[
8 = k \cdot (4^2)
\]
\[
8 = k \cdot 16
\]
\[
k = \frac{8}{16} = 0.5
\]
Both calculations confirm:
Thus, the value of \( k \) is \( \textbf{half} \) or \( 0.5 \).