The path of a soccer ball is modeled by the function h(x) = -0.005x2 + 0.25x, where h is the height in meters and x is the horizontal distance that the ball travels in meters. What is the maximum height that the ball reaches?

Question

phi · Answer

if this is calc, take the derivative, set equal to zero, and solve for x.  Plug x into h(x) to get the height.

anonymous · Answer

it says round to the nearest thousandth. 50 was not correct.

campbell_st · Answer

use the line of symmetry to find the max

x = -0.25/(2 x 0.005)    x = 25 is the line of symmetry.

find h(25) = -0.005(25)^2 + 0.25(25)

h = 3.125 metres

phi · Answer

did you try 0.25/(2*0.005) to find x ?

anonymous · Answer

i am so confused. 25 is wrong too.

anonymous · Answer

oohh. 3.125 meters. THANK YOU!

phi · Answer

25 is where h(x) is maximum.  To find the height, you have to replace x with 25 in the equation h(x)

campbell_st · Answer

lol.. 25 is correct all parabolas are symmetrical.... to find the line of symmetry use 
x = -b/2a which comes from the general quadratic formula


in your question b = 0.25, a =0.005   substitute them to find the line of symmetry

Once you know that... put the value into the original equation to find the height. |dw:1331063051964:dw|