Question

How is the graph of `y=8x^2-1` different from the graph of `y=8x^2`?

Answer 1

See below:

Explanation:

With the function `y=8x^2` (or really any function), we're taking a series of values of `x`, dropping them into the function, and getting a `y` value.

In this case, when `x=0, y=0`, when `x=1, y=8`, and when `x=-10, y=800`

So let's now look at `y=8x^2-1` - how is it different? For each value of `x` that we put into this function, the resulting value of `y` will be one less than for the other function.

This gives us when `x=0, y=-1`, when `x=1, y=7`, and when `x=-10, y=799`.

Graphically, they look like this (with the `y=8x^2` nested just above the `y=8x^2-1`):

graph{(y-8x^2)(y-8x^2+1)=0}

Answer 2

See below

Explanation:

A simple and short answer is that the first equation goes through `{0,-1}` as the `y`-intercept, but the second equation's `y`-intercept is the origin.

graph{y=8x^2-1 [-10, 10, -5, 5]}

graph{8x^2 [-10, 10, -5, 5]}