The problem states that $y$ varies directly as the square of $x$. We are given that $y=4$ when $x=1$. We are asked to find something, but it is cut off from the image. It's likely asking us to find the equation relating $y$ and $x$, or to find the value of $y$ for a given $x$, or vice versa. I will assume the problem asks to find the equation relating $y$ and $x$.

1. Problem Description

The problem states that $y$ varies directly as the square of $x$. We are given that $y=4$ when $x=1$. We are asked to find something, but it is cut off from the image. It's likely asking us to find the equation relating $y$ and $x$, or to find the value of $y$ for a given $x$, or vice versa. I will assume the problem asks to find the equation relating $y$ and $x$.

2. Solution Steps

Since $y$ varies directly as the square of $x$, we can write the relationship as:

$y = kx^2$

where $k$ is the constant of proportionality.

We are given that $y=4$ when $x=1$. We can substitute these values into the equation to find $k$:

$4 = k(1)^2$

$4 = k(1)$

$k = 4$

Therefore, the equation relating $y$ and $x$ is:

$y = 4x^2$

3. Final Answer

The equation relating $y$ and $x$ is $y = 4x^2$.