Question

How do you use the important points to sketch the graph of `5x^2 - 3x + 2`?

Answer 1

Find the points that are easy to find.

Explanation:

For `5x^2−3x+2`, you should take the easiest point possible: the point where x=0. `5(0^2)-3(0)+2` is equal to 0-0+2=2. Thus we know that one point is `(0, 2)`.
Then we could plug in a small random number such as 2.
`5(2^2)-3(2)+2`
`5(4)-6+2`
`20-6+2`
That will equal 16. So we know another point on our graph is (2, 16).
But since this is a parabola that faces up, we need another point.
`5(-1^2)-3(-1)+2`
`5(1)+3+2`
Hence we can infer another point is (-1, 10)
graph{5x^2-3x+2 [-40, 40, -20, 20]}

With the 3 points we have, we can draw the graph with artistic flair now.