Graphs of polynomial functions

[TonyHem]

9) A soccer player is performing sprint drills at a training session. There are three cones that he must reach. Two cones are positioned forward of his starting position and one is behind him. He must reach all three cones and return to his starting position in 10 seconds. His displacement is given by where x is the distance from his starting point at time t seconds.

a) given that (t-2) is a factor, find the other factors
b) sketch the graph of x against t for [0,10]
c) find the distance of the furthest cone ( correct to 2 decimal places)
d) Find the distance of the closest cone ( "                                    ")
e) Find the player's average speed over the 1st 10 seconds.

a) t(t-7)(t-10)
b) graph.
c) ?

any help appreciated.

[Damo17]

c) I would use the graph and use the calculator. From the graph you can see that the TP= (4.6, -7.75) below the x axis has the greatest y value along the graph meaning it's the furthest away.  therefore c) is 7.75 m.

d) use the graph again, the first max TP is what we want as the y-value along the curve for the first 10s would be the smallest there, and work out the y value which is 2.75 m.

This may not be the right/best way but it seems to work.

[TonyHem]

Yup I know it works on the calc. Just wondering if theres anyway to do it without one? If not then, its all good.

[shinny]

Use calculus to find the x co-ordinates of the TPs within [0,10] and then find their respective y co-ordinates. I think that should work. However, if this is in the 'graphs of polynomial functions' chapter and not the calculus one, I'm pretty sure they're just expecting you to calculator hack your way through it.