Question

How do you identify the important parts of `f(x)=x^2+3` to graph it?

Answer 1

`f(x)=x^2+3` is:
- a parabola
- concave upward
- centered at `x=0`
- shifted up by 3 units

Explanation:

First you can try to determine what kind of curve it is.

In this case, we see it's a polynomial of second degree, which means it will be a parabola .

To determine whether the parabola is concave upward or downward, check the sign of the term containing `x^2`. In this case it is positive, so the curve will be concave upward.

If the function was `(x-2)^2+3`, that would signify a shift of 2 units to the right. But it's not, so the parabola will be centered at `x=0`.

Finally, look at the constant term in the expression. `+3` means that the parabola will be shifted upward by 3 units.

To summarize, we expect `f(x)=x^2+3` to be a parabola, concave upward, centered at `x=0`, and shifted up by 3 units.

Let's check the graph:

graph{x^2+3 [-10.205, 9.795, -1.08, 8.92]}

Here we can see that we are correct!