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Question: Write the equation of a cubic function that has the x-intercepts of -4, 2, and 5 and passes through the point (6,20)

My Answer: y = .5x^3-1.5x^2-9x+20

What I did: Put the x-intercepts and given point into stat plot (on calculator) then hit stat -> calc -> cubic reg on calculator and was given that equation however it doesn't pass through the given point (6,20)

Can you help and tell me if I did anything wrong?

Thank You

4 answers

I will do mine using just a good ol' fashioned pencil and paper ...

intercepts are -4, 2, and 5
so
y = a(x+4)(x-2)(x-5)
The a will stretch it and force it to go through (6,20)
20 = a(10)(4)(1)
20 = 40a
a = 1/2

y = (1/2)(x+4)(x-2)(x-5)

Well, what do you know, I didn't even need my paper and pencil, just simple mental arithmetic
I see thanks for the help but what is the final equation? I had 1/2x^3-x.5x^2-9x+20
What is wrong with my "final" equation.
Why mess up a nice looking equation in factored form ??

your answer is correct, if you fix that typo in "-x.5x^2"
5/3,-5,-1 and passes through the point (0,50)