Sketching Polynomials

Sketching PolynomialsWhen drawing y = P(x)

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

23 211 e.g. xxxy

x

y

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant• x intercepts are the roots, solve P(x)=0

23 211 e.g. xxxy

x

y

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant• x intercepts are the roots, solve P(x)=0• as , P(x) acts like the leading termx

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

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant• x intercepts are the roots, solve P(x)=0• as , P(x) acts like the leading termx

• even powered roots look like or

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant• x intercepts are the roots, solve P(x)=0• as , P(x) acts like the leading termx

• even powered roots look like or

• odd powered roots look like or

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

23 211 e.g. xxxy

x

y

graph starts here graph finishes here

x

y

23 211 e.g. xxxy

Sketching PolynomialsWhen drawing y = P(x) • y intercept is the constant• x intercepts are the roots, solve P(x)=0• as , P(x) acts like the leading termx

• even powered roots look like or

• odd powered roots look like or

• if the curve can be written as , then it is a basic curve. nx a

2( ) 1 3 0ii x x

2( ) 1 3 0ii x x y

x1–3

2( ) 1 3 0ii x x y

x1–3

2( ) 1 3 0ii x x y

x1–3

Q: for what values of x is thecurve below the x axis?

2( ) 1 3 0ii x x y

x1–3

Q: for what values of x is thecurve below the x axis?

2( ) 1 3 0ii x x y

x1–3

Q: for what values of x is thecurve below the x axis?

3 or 1x x

Exercise 3B; 2, 3, 4ac, 5ac, 6bdg, 7ac, 8