Quadratic model problem solving

Question

The function y= -0.03(x - 14)^{^2}+ 6 models the jump of a red kangaroo where x is the horizontal distance (in feet) and y is the corresponding height (in feet). What is the kangaroo's maximum height? How long is the kangaroo's jump?

Answer 1

In a quadratic function, the maximum or minimum occurs at the vertex of the function.  A quadratic in vertex form is

 

y = a(x - h)² + k

 

where:

a is the coefficient of the x² term

The vertex has coordinates (h, k)

 

a = -0.03

h = 14

k = 6

 

The vertex is (14, 6).  Because the value of a is negative coefficient, the function will have a maximum.

 

So the kangaroo's maximum height will be 6 feet at a horizontal distance of 14 feet.

Answer 2

Since the term -0.03(x-14)² is has a negative coefficient (-0.03), the biggest value it can have is 0. So the maximum height would be when x = 0 and y = 6.