Question

why are these equations poor models of hitting a baseball:

y= -0.002x(x-433.1)

I get maximums of (216,93). Other problems' maximums are in the (220, 100)range. So are they poor models because the distance and heights are unreasonable?

2) Why is the constant a in y=ax^2 + bx + c negative in a reasonable model?
is it because the graph is then a hill versus a valley?

Answer 1

1. Plenty of players hit the ball 400 feet or more. This function has roots at 0,433, so it appears to model typical hitting ability.

2. negative a means that there is a downward force acting on the ball: gravity. so, yes, the graph is a hill. The ball takes off at some speed, but gravity slows down its ascent and makes it drop back to earth.

Answer 2

y= -0.002x(x-433.1)
is
y = .8662 x - .002 x^2
I do not see anything very wrong except that the baseball does not start out at zero height. When x = 0 y should be like one meter high so I might prefer something like
y = 1 + .8662 x - .002 x^2

Yes, coef of x^2 must be negative because as x gets big the ball must drop.