Question

A football is kicked from the ground and travels at a rate of 10 meters per second. The function 𝑓(𝑥)=10𝑥−5𝑥2 represents the ball's height above the ground at x seconds. Based on this function model, what is the football's highest point and how long will it take to hit the ground?

Answer 1

I think that the ball will reach 400 meters at the highest point and the ball will hit the ground in 40 seconds. Is this correct?

Answer 2

the max is on the axis of symmetry of the parabola

x = -b / 2 a = -10 / (2 * -5) = 1

1 second up, one second down ... 2 sec flight time

plug one into the original equation to find max height

Answer 3

F(x) = 10x-5x^2.
a. V^2 = Vo^2+2g*h = 0.
10^2+(-20)h = 0
h = 5 m. = max. ht.

b. 10x-5x^2 = 0 when the ball hits gnd.
Divide both sides by 5x:
2-x = 0
X = 2 s. to hit gnd.

Answer 4

a. Yes, the original Eq should be used to calculate max. ht. :
h max = 10x-5x^2 = 10*1-5*1^2 =