Trajectory of an angry bird. Given the screenshot below, find a piecewise define

Question

Trajectory of an angry bird. Given the screenshot below, find a piecewise defined function... see below!

Later in the game, a new bird is introduced (small triangular bird) which changes its trajectory from a parabola to a line when you tap the screen. This is a useful tool if you misjudge initially. Given the screen shot below, find a piecewise defined function which describes the piecewise trajectory of the bird that hits bird D. Be sure to include the domain for each piece. f(x) = { All of this parabolic pleasure seeking is something you may want to think about when you ask yourself if you will ever use any of this quadratic stuff outside of school. You might not be number crunching, but every time you toss something across the room to the trash can or play games like Angry Birds, you're subconsciously solving for the roots of a quadratic equation.

Explanation / Answer

finding the eqiation from the 3 points given

( 2,5) ( 0,0) ( 3,6)

y = ax^2 + bx + c

plugging each value of x and y in the function and finding a,b,c

we get function as

y = -1/2 x^2 + 7/2 x

finding other function

equation of line from 2 points ( 5.5, 4.125 ) and ( 11,0.5)

y = -29/44 x + 31/4

now defining the piecewise function

f(x) = { -1/2 x^2 + 7/2 x   if x <= 3

  -29/44 x + 31/4 if x >= 4.5 }

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