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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