Can anybody help me write the equation of this graph. How can I do it myself?
1 Answer
Feb 12, 2018
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]}