Problema Solution
Cory is training his dog, Cocoa,for an agility competition. Cocoa must jump through a hoop in the middle of a course. The center of the hoop is 8 feet from the starting pole. The dog runs from the starting pole for 5 feet, jump through the hoop,and lands 4 feet from the hoop. When Cocoa is 1 foot from landing, cory measures that she is 3 feet off the ground. Write a function to represent Cocoa's height in terns of her distance from the starting pole
Answer provided by our tutors
we will set Cartesian coordinate system with origin at the starting pole
the height of Cocos jump will be a quadratic function written in factored form
h(x) = a(x - x1)(x - x2), where x1 and x2 are the roots of the quadratic equation
for the roots we know x1 = 5, x2 = 12 that is the distances from the starting pole before and after the jump
h(x) = a(x - 5)(x - 12)
also we now that 1 foot from landing Coco is 3 feet off the ground this means we have the following point of the graph (11, 3) and if we replace these values in the above equation we get
3 = a(11 - 5)(11 -12)
a*6(-1) = 3
a = -0.5
thus the equation is
h(x) = -0.5(x - 5)(x - 12)
see the graph of Cocos path by clicking here