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

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1 Answer
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]}