CURVE SKETCHING - FCAMPENA...Curve Sketching of Polynomial in Factored Form In geometry, curve...
Transcript of CURVE SKETCHING - FCAMPENA...Curve Sketching of Polynomial in Factored Form In geometry, curve...
Curve Sketching of Polynomial in Factored Form
In geometry, curve sketching
(or curve tracing) includes
techniques that can be used to
produce a rough idea of overall
shape of a plane curve given its
equation without computing a
large numbers of points
required for a detailed plot.
Basic Techniques of Curve Sketching
Determine the x- and y- intercepts of the curve.
Determine the symmetry of the curve.
wrt the x-axis? y-axis? origin?
Determine the end behavior.
As π β Β±β, π β?
Determine the shape of the graph near a zero.
If the multiplicity of the zeros is odd, then the graph will cross the x-axis at the zeros. Otherwise, it will not cross the x-axis.
Examples
1. π¦ = π₯3 β 4π₯
2. π¦ = β(π₯ β 2)2 (π₯ β 4)
3. π¦ = π₯3 β 2π₯2 β 4π₯ + 8
4. π¦ = (π₯ β 2)(π₯ + 4)3 (π₯ + 1)2
To which conics are the following
radical equations related to
π¦ = Β± ππ₯ β β π¦ = Β± β β π₯2 π¦ = Β± β β ππ₯2 π¦ = Β± β + ππ₯2
π¦ = Β± β β ππ₯
Example
1. π¦ = π₯
2. π¦ = β π₯ + 3 β 5
3. π¦ = π₯2 β 3π₯ β 4 β 5
4. π¦ = 4 β π₯ β 5
5. π¦ = π₯2 β 9
Sketch
1. y = (x-2)(x+4)2 (x+1)
2. y = (x-2)2(x+4)2 (x+1)
3. y = (x-2)(x+4) (x+1)2
4. y = (x-2)(x+4)3 (x+1)2
Write equation for