Question

A boy throws a stone into a lake from a 74 foot high wall. The chart gives the horizontal distance, x (in feet), the rock has traveled from Jesse and the height, y (in feet) of the rock above the lake.

Distance, x: (14) (24) (41) (55)
Height, y: (86.43) (91.36) (92.19) (85.75)

Write the equation that best fits the path of the rock from Jesse to the lake below.

I wasn't at school when we were taught this and the notes I have mention nothing of this. I am completely lost, can someone help?

Answer 1

I will assume you want your data to fit an equation of the type

y = ax^2 + bx + c

from the first "point" (14,86.43)
86.43 = 196a + 14b + c , (#1)
from the 2nd:
91.36 = 576a + 24b + c , (#2)
from the 3rd:
92.19 = 1681a + 41b + c , (#3)

#2 - #1:
4.93 = 380a + 10b -----#4
#3 - #2
.83 = 1105a + 17b ---- #5

#4 times 17 -----> 83.81 = 6460a + 170b
#5 times 10 -----> 8.3 = 11050a + 170b
subtract them
-75.51 = 4590a
a = -.01645
in #4:
4.93 = 380(-.01645) + 10b
b = 1.11814
in #1
86.43 = 196(-.01645) + 14(1.11814) + c
c = 74
<b>y = -.1645x^2 + 1.11814x + 74</b>

testing for point not used:
(55,85.75)
RS = -.01645(55^2) + 1.11814(55) + 74
= 85.73
the given data was 85.74 , not bad