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.
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
1 Answer
Nov 20, 2017
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]}