Exercise 94 Page 461

When we know the roots of a polynomial function, we can write it in factored form. Since it has three roots, we get three factors. Factored Form [-1em] y= k(x- 3)(x- 2)(x-( -1)) &Vertical Stretch: k &First Root: 3 &Second Root: 2 &Third Root: -1To complete the function we must also find the vertical stretch k. We can do that by substituting the known point (1,1) into the function and solving for k.

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

SubstituteII

x= 1, y= 1

1=k( 1-3)( 1-2)( 1-(-1))

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Solve for k

SubNeg

a-(- b)=a+b

1=k(1-3)(1-2)(1+1)

AddSubTerms

Add and subtract terms

1=k(-2)(-1)(2)

Multiply

Multiply

1=4k

RearrangeEqn

Rearrange equation

4k=1

DivEqn

.LHS /4.=.RHS /4.

k=1/4

Now we can complete the function. Notice that we will remove the parenthesis around -1. y=1/4(x-3)(x-2)(x+1)