Quadratic equations help please

Question

the path of a soccer ball can be modelled by the function h(d)=-0.1d²+0.5d+0.6, where h is the height of the ball and d is the horizontal distance from the kicker, both in metre.

a)what are the zeroes of the function?

b)use the quadratic equation 0=-0.1d²+0.5d+0.6 to determine the horizontal distance that a ball travels after being kicked. How far did the ball travel downfield before it hit the ground?

Answer 1

(a)

For zeros of the function, solve:

 

0 = -0.1d2+0.5d+0.6

=> d2 -5d - 6 = 0 (multiply both sides with -10)

 

apply quadratic formula:

d = (5 ± √25 - 4*1*(-6) ) / 2

d = (5 ± √49 ) / 2
d = (5 ± 7 ) / 2

d = 6, or -1, these are your zeros of the function.

 

(b) After being kicked, ball goes in a downward facing parabolic trajectory (check link at the end for more details), with the equation:

 

h(d)=-0.1d2+0.5d+0.6

here h is height and d is horizontal distance traveled by the ball.

 

When ball hits the ground, it's height would be zero, i.e. h = 0,

that means, you need to solve the equation: 0 = -0.1d2+0.5d+0.6

which you already did in (a) and got

d = 6 meters

(-1 meters does not make sense for the distance traveled by the ball)

 

 

http://jwilson.coe.uga.edu/emt725/class/sarfaty/emt669/instructionalunit/parabolas/parabolas.html