Answer:
The Equation is y = -0.1( x - 26 )² + 20
Step-by-step explanation:
Given:
Starting position of the bird = ( 10 , 0 )
Final position of the bird = ( 42 , 0 )
Maximum Height of the bird = 20 yards
To find: Equation that represent this condition.
Clearly, Birds flight path is not a straight line. It has a curved path.
So, the path bird follow is a PARABOLA.
Standard Equation of the parabola in vertex form, y = a( x - h )² + k
where ( h , k ) is the vertex of the parabola.
In our Question , vertex is the point at the highest position.
Vertex will be 20 yard above the mid point of the starting and final position.
Using Mid-Point Formula,
Mid-Point of ( 10 , 0 ) & ( 42 , 0 ) = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{10+42}{2},\frac{0+0}{2})=(26,0)[/tex]
Now, the vertex = ( 26 , 0 + 20 ) = ( 26 , 20 )
⇒ Equation, y = a( x - 26 )² + 20
Now, we find value of by substituting value of (10 , 0) in the equation,
⇒ 0 = a( 10 - 26 )² + 20
a( -16 )² = -20
a(256) = -20
a = -20/256
a = −0.078125
a ≈ -0.1
Therefore, The Equation is y = -0.1( x - 26 )² + 20
