11 x1 t15 02 sketching polynomials (2013)

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant

23 211 e.g. xxxy

x

y

When drawing y = P(x) • y intercept is the constant• x intercepts are the roots

Sketching Polynomials

23 211 e.g. xxxy

x

y

When drawing y = P(x) • y intercept is the constant• x intercepts are the roots• as , P(x) acts like the leading termx

Sketching Polynomials

23 211 e.g. xxxy

x

y

23 211 e.g. xxxy

x

y

graph starts here

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

When drawing y = P(x) • y intercept is the constant• x intercepts are the roots• as , P(x) acts like the leading termx• even powered roots look like or

Sketching Polynomials

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

When drawing y = P(x) • y intercept is the constant• x intercepts are the roots• as , P(x) acts like the leading termx• even powered roots look like or

• odd powered roots look like or

Sketching Polynomials

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

x

y

23 211 e.g. xxxy

When drawing y = P(x) • y intercept is the constant• x intercepts are the roots• as , P(x) acts like the leading termx• even powered roots look like or

• odd powered roots look like or

Sketching Polynomials

• If the polynomial can be written as , then it is a basic curve nx a

2211 e.g. 234 xxxxy

2211 e.g. 234 xxxxy

x

y

Exercise 4B; 3cei, 4deghi, 6acm 7ac, 8, 11