50 Points Per Answer Create a function in factored form for a roller coaster.

• Your coaster ride must have at least 3 relative maxima and/or minima
• The ride length must be at least 2 minutes (blueprint must use seconds)
• The coaster ride starts at 250 feet
• The ride dives below the ground into a tunnel at least once
• The ride must have one “turn around/bounce” (Mutliplicity 2)
• The ride must have at least one “twist/swerve” (Multiplicity 3)
• The ride must hit ground level at least three times (Three real zeros)

Since you have 3 local extremas, you will have a polynomial function of degree 4.  The domain of the function is [0, 4].

Use these initial conditions as your guidelines:

f(0) = 250

f(x) has at least one x-intercept (crosses the x-axis) and must be in the interval (0, 4].

f(x) decreases in any of the following intervals: (0, 1) or (2, 3)

Remember, you will have an arbitrary function that satisfies these conditions.

Step-by-step explanation:

I did :Your coaster ride must have at least 3 relative maxima and/or minima

there are no short passages to look at

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)