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

Mar 26, 2018

$f \left(x\right) = {x}^{2} + 3$ 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 ${\left(x - 2\right)}^{2} + 3$, 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 $f \left(x\right) = {x}^{2} + 3$ 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!