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

1 Answer
Sharkbasket
Mar 26, 2018

#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!

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