Question

How is the graph of `y=1/3x^2-4` related to the graph of `f(x)=x^2`?

Answer 1

The lines intersect
`(sqrt(6),6)(-sqrt(6),6)`

Explanation:

f(x) is the expression used for functions. It is another way of showing the y value because it depends on the variable x. The y value is created after the x value is put through the function

Thus

`f(x) = x^2` is the same as `y = x^2`

Both equation have y as their subjects. This way an inequality can be created.

`x^2=1/3x^2-4`

Make x the subject

`x^2+4=1/3x^2`

`3x^2+12=x^2`

`2x^2 = -12`

`x^2=-6`

`x=+-sqrt(6)`

Once the x coordinate has been found, the y one can be found two. There are two values of x so there are also two coordinates.

`(sqrt(6),6)(-sqrt(6),6)`