Graphing polynomials part 1

R=4 because p(−1)=4

R=2 because p(−1)=2

R=1 because p(−1)=1

R=0 because p(−1)=0

No, because leading term is positive

Yes, because degree is even

No, because p(−1)≠0

Yes, because p(−1)=0

x=3 from the factor (x−3)

x=2 from the factor (x−2)

x=1 from the factor (x−1)

x=0 from the factor x

$$−3x(x−2)^2(x−3)$$

$$-3x(x-1)^2(x-3)$$

$$-3x(x-3)^2(x-2)$$

−3x(x−1)(x−2)(x−3)

x=0,1,3 with x=1 double root

x=0,2,3 with x=2 double root

x=0,2,3 with multiplicity one each

x=0,1,2 with multiplicity one each

A distance where slope is zero

A point of maximum speed on track

A location where track is highest point

A distance where height is zero yards

x = −3 with multiplicity 2

x = 3 with multiplicity 4

x = −3 and x = 3 simple

x = 3 with multiplicity 2

x = −3 with multiplicity 4

Crosses straight through x = −3

Touches and turns at x = −3

Oscillates near x = −3

Has a vertical asymptote at −3

Has a hole at x = −3

End behavior depends only on zeros

Both graphs have same-end behavior

Neither has predictable end behavior

Odd degree: same ends, even degree: opposite ends

Odd degree: opposite ends, even degree: same ends

Rise right, fall left

Fall right, fall left

Rise right, rise left

Fall right, rise left