Question

The function pictured has the form of y=k(x^2). What is the value of k
?

The points ploted on the graph are (-4,4) (4, 4) (-2, 1) (2,1)


answers

2

1

1/4

1/2

Answer 1

To determine the value of \( k \) in the function \( y = k(x^2) \), we can use one of the points given on the graph. Let's choose the point \( (2, 1) \) to find \( k \).

We know that at the point \( (2, 1) \):

\[
y = 1 \quad \text{and} \quad x = 2
\]

Substituting these values into the function gives:

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

This simplifies to:

\[
1 = k(4)
\]

Now, to solve for \( k \):

\[
k = \frac{1}{4}
\]

Thus, the value of \( k \) is \( \frac{1}{4} \).

To ensure this value is consistent with the other points given, we can check:

1. For \( (-2, 1) \):

\[
y = k(-2^2) = \frac{1}{4}(4) = 1 \quad \text{(Correct)}
\]

2. For \( (4, 4) \):

\[
y = k(4^2) = \frac{1}{4}(16) = 4 \quad \text{(Correct)}
\]

3. For \( (-4, 4) \):

\[
y = k(-4^2) = \frac{1}{4}(16) = 4 \quad \text{(Correct)}
\]

Since \( k = \frac{1}{4} \) satisfies all the points, the final answer is:

\[
\text{The value of } k \text{ is } \frac{1}{4}.
\]