The height of a thrown object as a function of the horizontal distance that it has traveled is a quadratic function. An object is thrown from ground level, 63 m away from the base of a tower 17 m high and just barely clears the top of the tower. it lands 63 m on the other side. Find the quadratic function that represents this.

My work so far:
h(d)=ad2 + bd + c
17=(63)2a + (63)b 0=(126)2a + 126b
17=(3969)a + 63b 0= 15876a + 126b
after this i'm stuck

Question

The height of a thrown object as a function of the horizontal distance that it has traveled is a quadratic function. An object is thrown from ground level, 63 m away from the base of a tower 17 m high and just barely  clears the top of the tower. it lands  63 m on the other side. Find the quadratic function that represents this.

My work so far:
h(d)=ad2 + bd + c
17=(63)2a + (63)b   0=(126)2a + 126b
17=(3969)a + 63b    0= 15876a + 126b
after this i'm stuck

anonymous · Answer

h(d)=ad^2+bd+c

 (g is gravitational acceleration

63=-b/2a (the top point)
b=-126a

c=0 (at the initial point, the height is 0)

17=a(63)^2+ 63b

17=a*63^2-126*63a

a=-17/(63^2)

b= 34/63

h(d)=(-17/3969)d^2+34b/63

aryavegapunk · Answer

it would just be 34/63 and not 34b/63 right?

aryavegapunk · Answer

@marsss

anonymous · Answer

it's 34d/63. i'm so sorry.

aryavegapunk · Answer

It's alright, Thank you so much!!

anonymous · Answer

welcome my punker friend :)