How do I identify characteristics of a parabola [from] a table …
Hi AFK. We examine given data points while thinking about previously-learned characteristics of parabolas, to see whether we can recognize any patterns we've learned before. Plotting the points on paper may help.
I don't what you've already learned about parabolas. So, if you don't understand some of the concepts below, you may ask for explanation or try looking them up (in a textbook or on the Internet).
Your example contains two points: (1,3) and (5,3).
The y-coordinates are the same. That tells us: y is a function of x. Therefore, we know the parabola does not open to the left or right.
The given points lie on a horizontal line. We can determine their midpoint. Therefore, we know the parabola's axis of symmetry; we can state the x-coordinate of the vertex. By taking cases, we can comment on the y-coordinate (eg: if the parabola opens downward, y>?).
If you're learning about parabolas as conic sections, then you may have additional characteristics to ponder.
Cheers ?
