Question

What is the graph of `f(x) = 3x^2`?

Answer 1

Our vertex is `(0,0)`, and our next two points (which will help dictate the "slope") are `(-1,3)` and `(1,3)`

Explanation:

We need a few things to graph this: the `x` and `y` intercepts and the "slope". Because `x` is squared, I know that this will be a quadratic function. There aren't slopes for quadratics, but we can look for certain points.

First, let's look for `y`-intercepts:
`y=ax^2+bx+color(red)(c)`In our equation `(y=3x^2)`, we don't have a last constant, so our `y`-intercept is `0`.

Now let's look for our `x`-intercept. To find it, we set `y=0` and solve for `x`:
`0=3x^2`
`0=x^2`
`sqrt(0)=sqrt(x^2)`
`x=0`

So, our `x` and `y` intercepts are both `0`, which means our vertex is `(0,0)`

Now we have two out of our three required pieces. Now let's think this next one through...
If we start at `(0,0)` and move up one, our `x=1`:
`y=3(1)^2`
`y=3`
That means our point is `(1, 3)`.

Now let's solve for when `x=-1`:
`y=3(-1)^2`
`y=3`
So, our second point is `(-1,3)`

We can solve for more points this way, but for the most part, having three reference points to draw from are enough.

Our vertex is `(0,0)`, and our next two points (which will help dictate the "slope") are `(-1,3)` and `(1,3)`

graph{y=3x^2}