Create a polynomial function that could represent a roller c

Create a polynomial function that could represent a roller coaster. The roller coaster would start at 250 ft., have at least 3 relative extremeas, and would last at least four minutes

Solution

to have \"3 relative maximums or minimums\" the grade of the polynomial must be at least 4,
and to have an additional maximum or minimum, the grade of the polynomial must be at least 5.

y = k(x-4)(10x+3)(2x-2)(x+1)(x-2.5)

Roller coaster would start at 250 ft : y intercept = 250 ft

250 = k(-4)(3)(-2)(1)(-2.5)

k = -250/60 = 25/6

y = (25/6)(x-4)(10x + 3)(x-2)(x+ 1)(x-2.5)

Above is factored form.