Question

The function pictured has the form of y=k⋅x^2
. What is the value of k? The points on the graph (-4.8) (4,8) (-2, 2) (2,2)



(1 point)
Responses

2

12

0

0.2

-2

Answers

GPT-4o mini
To determine the value of \( k \) in the function \( y = k \cdot x^2 \), we can use one of the given points on the graph. Let's choose the point \( (2, 2) \).

1. Substitute \( x = 2 \) and \( y = 2 \) into the equation:

\[
2 = k \cdot (2^2)
\]

2. This simplifies to:

\[
2 = k \cdot 4
\]

3. Now, solve for \( k \):

\[
k = \frac{2}{4} = 0.5
\]

We can try another point to confirm.

Let's use the point \( (-2, 2) \):

1. Substitute \( x = -2 \) and \( y = 2 \):

\[
2 = k \cdot (-2)^2
\]

2. This also simplifies to:

\[
2 = k \cdot 4
\]

3. Solving for \( k \) again gives:

\[
k = \frac{2}{4} = 0.5
\]

However, this value does not match any options. Let's check a point with a different \( y \) value, such as \( (-4, 8) \):

1. Substitute \( x = -4 \) and \( y = 8 \):

\[
8 = k \cdot (-4)^2
\]

2. This simplifies to:

\[
8 = k \cdot 16
\]

3. Solving for \( k \):

\[
k = \frac{8}{16} = 0.5
\]

We got consistent results, but it doesn't match any of the provided options. Therefore, let's use the point \( (4, 8) \):

1. Substitute \( x = 4 \) and \( y = 8 \):

\[
8 = k \cdot (4)^2
\]

2. This becomes:

\[
8 = k \cdot 16
\]

3. And solving for \( k \):

\[
k = \frac{8}{16} = 0.5
\]

The value of \( k \) consistently comes out to \( 0.5 \), which is not listed in your options. If the function form and values provided are correct, there may be an error with the options. However, based on calculations, the value of \( k \) would be \( 0.5 \).

Given the options you provided, please check if there is a mistake in the point coordinates or the form of the function, as none of the options align with the calculated \( k \).

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