Question

An archer releases an arrow from a shoulder height of 1.39 m. When
the arrow hits the target 18 m away, it hits point A. When the target is
removed, the arrow lands 45 m away. Find the maximum height of the
arrow along its parabolic path. Assume Point A is 1.28 m from the ground. (The top of the target was 1.52 m and point A is 24 cm from the top so 1.52 - .24 = 1.28 m). You now know the coordinates of 3 points on the parabolic path. You know the coordinates of the starting point and point A and the landing point. The x coordinate is the distance from the target along the ground and the y coordinate is the height above the ground. You can know find the quadratic equation through these 3 points using the graphical calculator. Once you have the equation find the maximum height

Answer 1

Use the equation of position: \(\sf \color{red}{f(x) = ax^2+bx+c}\)
is this somehow ringing a bell?

Answer 2

wut? this makes absolutely no sense whatsoever to me

Answer 3

can i has a step by step?

Answer 4

An archer releases an arrow from a shoulder height of 1.39 m, meaning (0, 1.39)
When the arrow hits the target 18 m away, it hits point A.
The target is 1.5 m tall, meaning (18, 1.5)
Note: You may have to adjust the 1.5 depending on where point A is on the target)
When the target is removed, the arrow lands 45 m away.
(45, 0)

Answer 5

\(\sf \color{red}{y = f(x) = ax^2+bx +c}\)

Answer 6

as abbot is doing you can find equation algebraically
since the question asks you to use graphing calculator you can also input the 3 points in a list then under "stats" "calc" "quadreg" it will fit a parabola to the 3 given points

Answer 7

I didn't even read that far ahead, @dumbcow long question is too dam long.

Answer 8

omg so basically i just put those 3 points in my TI-84 and it does the work for me? o.O wow im so slow *facepalm*