Question

You shoot an arrow set a target. The parabolic path of the arrow passes through the points shown in table.

X. Y
30. 6
60. 7
100. 4
A. Find a quadratic function in standard form that models the path of the arrow. Then graph the function. Use quadratic regression for this step. The three points satisfy a quadratic function of form y= ax^2 +box +c

Answer 1

900a+30b+c=6....(1)

3600a+60b+c=7...(2)

10000a+100b+c=4....(3)

(2)-(1)

2700a+30b=1.....(4)

(3)-(1)

9100a+70b=-2...(5)

solving (4) and (5) then putting a, b into (1)

a=-13/8400, b=29/168, c=31/14

The graph is like a parabola with upward dome, it's head at upside and two legs downwards.