Example of a Horizontal Parabola: x=ay²

Function of a Parabola

Sideways Stuff

In a parabola of form $y = ax^2$, the parabola opens up or down, depending on $a$. For each value of $x$, there is only on possible value for $y$. Thus, this parabola is a function as it opens down. However, in this parabola we realize that for each $x$, there is a possibility of two $y$'s! For example, if we have an $a$ of one and an $x$ of $4$, we have the equation, $4 = 1(y^2)$. Solving, we find that $y$ can be either $-2$ or $2$. If $a$ is positive, as it gets bigger, so will the $y$. If $a$ is negative, as it gets smaller, so will the $y$. (There is a difference) For example, we have two graphs:

$$x = y^2$$

$$x = -y^2$$

As you can see, these parabolas are not functions, since there is more than one $y$ value for each $x$ value.