How to work out the function of a quadratic ?

Question

Working out the path of rocket.

Its Parabola (quadratic)

The rocket is launched at point 0,0..........lands back at 15,0

Turning point is at 7.5,140.625

What is the funtion that describes the stuff above.

Show working out pls.

Urgent

Answer 1

quadratic: ax^2+bx+c

crosses 0,0 so if x=0 then y=0 ,  y=ax^2+bx+c ==> c=0

y=ax^2+bx

dy/dx=2ax+b

at turning point dy/dx=0 therefore:

2ax+b=0 , x=7.5 as stated

15a+b=0 ==============> equation number 1

also at 7.5 y=140.625

so ax^2+bx=a*7.5^2+b*7.5=140.625

56.25a+7.5b=140.625 divide both sides by 7.5 u'd get

7.5a+b=18.75 ============>equation number 2

u now just have to find value of a and b by solving the simultaneous euqations:

7.5a+b=18.75   double both sides

15a+b=0

15a+2b=37.5   (1)

15a+b=0          (2)

(1)-(2) ==> b=37.5

15a+37.5=0

a=-37.5/15=-2.5

so y=-2.5x^2+37.5x