Find a possible formula for a polynomial f with the given properties?

f has degree ≤2, f(0)=f(2)=0 and f(4)=48

How would I find a formula for f(x)=?
I tried to search for similiar questions online but I'm still really confused on how to solve this problem. All I now is that you use #y=ax^2+bx+c# to somehow solve this problem.

1 Answer
Jim G.
Nov 20, 2017

#y=6x^2-12x#

Explanation:

#f(0)=f(2)=0" indicate that" #

#x=0" and "x=2" are roots of the polynomial"#

#rArrx" and "(x-2)" are factors of the polynomial"#

#"the product of the factors express the polynomial"#

#rArry=ax(x-2)larrcolor(blue)"a is a multiplier"#

#"to find a substitute the point "(4,48)" into the equation"#

#48=4a(2)=8arArra=6#

#rArry=6x(x-2)#

#rArry=6x^2-12xlarrcolor(red)"in standard form"#
graph{6x^2-12x [-10, 10, -5, 5]}

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