Can anybody help me write the equation of this graph. How can I do it myself?

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1 Answer
Jim G.
Feb 12, 2018

#p(x)=1/24x^4-1/6x^3-2/3x^3+2/3x+2#

Explanation:

#"given the roots of a polynomial, say"#

#x=a,x=b" and "x=c#

#"then the factors are"(x-a),(x-b)" and "(x-c)#

#"the polynomial is the product of the factors"#

#rArrp(x)=k(x-a)(x-b)(x-c)larrcolor(blue)"k is a multiplier"#

#"identify the roots from the graph"#

#x=-2("multiplicity 2"),x=2" and "x=6#

#"factors are expressed as"#

#(x+2)^2,(x-2)" and "(x-6)#

#rArrp(x)=k(x+2)^2(x-2)(x-6)#

#"to find k use any other point on the graph"#

#"using the point "(0,2)" substitute into the equation"#

#2=k(4)(-2)(-6)=48krArrk=2/48=1/24#

#rArrp(x)=1/24(x+2)^2(x-2)(x-6)#

#color(white)(rArrp(x))=1/24(x^4-4x^3-16x^2+16x+48)#

#color(white)(rArrp(x))=1/24x^4-1/6x^3-2/3x^2+2/3x+2#
graph{1/24x^4-1/6x^3-2/3x^2+2/3x+2 [-10, 10, -5, 5]}

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