What do we already know about polynomial functions They are either ODD functions They are either EVEN functions Linear y 4x 5 Cubic y 4x 3 5 Fifth Power y 4x 5 x 5 Quadratics ID: 730429
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Slide1
Creating Polynomials
Given the Zeros.Slide2Slide3Slide4Slide5Slide6
What do we already know about polynomial functions?
They are either ODD functions
They are either EVENfunctions
Linear
y = 4x - 5Cubicy = 4x
3 - 5
Fifth Powery = 4x5 –x + 5
Quadraticsy = 4x2 - 5
Quartics
y = 4x
4
- 5
Quadratics
y = 4x
2
- 5Slide7
We know that factoring and then solving those factors set equal to zero allows us to find possible x intercepts.
TOOLS WE’VE USED
Factoring
Quadratic Formula
Long Division (works on all factors of any degree)
Synthetic Division (works only with factors of degree 1)
GCF
(x + )(x + )
The “6” step
Grouping
p/q
Cubic**Slide8
We know that solutions of polynomial functions can be rational, irrational or imaginary.
X intercepts are real.
Zeros are x-intercepts if they are realZeros are solutions that let the polynomial equal 0Slide9
We have seen that imaginaries and square roots come in pairs ( + or -).
So we could CREATE a polynomial if we were given the polynomial’s zeros.Slide10
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
-1, 2, 4
Step 1: Turn the zeros into factors.
(x+1)(x- 2)(x- 4)Step 2: Multiply the factors together.
x3 - 5x2 +2x + 8
Step 3: Name it!f(x) =x
3 - 5x2 +2x + 8Slide11
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
Step 1: Turn the zeros into factors.
Must remember that “
i”s
and roots come in pairs.
Step 2: Multiply factors.Slide12
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
Step 1: Turn the zeros into factors.
Must remember that “
i”s
and roots come in pairs.
Step 2: Multiply factors.Slide13
x 2
i
x
2
-
i
x
2
2x
ix
2i
4
2x
-ix
-2i
i
2
-1
x
x
x
x
(x
2
+ 4x + 3)
x 2
x
2
x
2
2x
4
2x
-3
x
x
x
x
(x
2
+ 4x + 1)Slide14
x
2
4x
1
x2+ 4x + 3
x44x3
-3f(x) = x
4+ 8x3 + 20x2 +16x + 34x
3
x
2
16x
2
3x
2
12x
3
4x