Good old st. Nick needs your help getting from Andria's house to Tong's house on Xmas eve. Of course that means rooftop to rooftop. with your knowledge of parabolars, santa has asked you to guide his sleigh (poor rudolph). It is 300 feet between their rooftops and there is a really big tree halfway between their house that stands 190 feet above the roof levels. If santa must fly a parabolic oath and he wants to just clear the tree, what would be the equation of the parabola that he would enter into his on-board computer? HINT DRAW A PICTURE.
I can not draw you a picture. However I will describe how you could draw the parabola.
We will assume that the tree is the y-axis.
The tree stands 190 feet above the roof.
Then the maximum of the parabola is the point ( 0, 190)
Now the distance between the roofs will represent the distance on the x-axis.
The distance is 300 feet.
The tree is half way between the roofs.
==> The roofs if 150 feet from the origin point if opposite directions.
Then the points ( 150, 0) and ( -150, 0) represent the roofs.
Then, The parabola is facing down .
==> y = -ax^2 + b
We will substitute the point (0, 190)
==> y(0) = b = 190
==> y = -ax^2 + 190
Now we will substitute with (150, 0)
==> y( 150)= -a(150)^2 + 190 = 0
==> a = 190/ 150*150 = 19/2250
==> y= (-19/2250) x^2 + 190