How to Find the Polynomial Function from a Graph

Introduction

Really liked the last chapter on Graphs so hoping. The question posed was how to Find the Polynomial Function from a Graph given

Solving

So first we derive the factors which is ezzy pezzy.

y = a(x-1)(x-2)(x-3)

Now we know this is a 4th degree polynomial so x⁴. The next step is to decide which of the 3 factors is multiplicity 2. We do this be looking at the graph. We know the crossing the x-axis is multiplicity 1, so the (x-2) and (x-3) are one. Therefore (x-1) is multiplicity 2 so (x-1)² as 1 + 1 + 2 = 4 = the degree of the polynomial.

So we now just need to find the a value. So we plug in the numbers we were given for x value of 0 or f(0), the value of the function is 36 or

36 = a(0-1)²(0-2)(0-3)
36 = a (1)(-2)(-3) = 6
 6 = a

So now we have

   = 6(x-1)(x-1)(x-2)(x-3)

...

   = 6x⁴-42x³+102²-102x+36