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Unit 16 Day 2 Polynomials
Do before time runs out!
[1] Take out your packet [2] Grab a chromebook [3] Complete Quiz #1 in GC [4] Complete warm upUsing finite differences, determine the degree of the following polynomials.
x y1. 2. x y
-10123
162
-2420
1
45
23
-6-14914
Any questions from the Homework?
Unit 16 Day 2 Polynomials
Unit 16 Day 2 Polynomials
Unit 16 Day 2 Polynomials
Unit 11 Day 1: Polynomials
I can find the x,y intercepts of a polynomial equation
I can convert from factored to general form
I can solve for the scale factor of a polynomial
Polynomial Functions
Quadratic: f (x) = 3x2 + 5x – 7
Cubic: f (x) = 7x3 5x2 + 3x – 1
Quartic: f (x) = 2x4 6x3 + 2x + 5
Quintic: f (x) = 11x5 2x2
Recall:
Unit 16 Day 2 Polynomials
Polynomial FunctionsHow does the degree relate to the shape?
Identify the xintercepts and degree, then write a possible equation.
Unit 16 Day 2 Polynomials
An nth degree polynomial function has exactly n zeros.
FUNDAMENTAL THEOREM OF ALGEBRA
(both real and complex)
What is the connection between the # of roots and the degree of the polynomial?
Sketch a graph for the following scenarios:
1. A quadratic function with 2 real roots.
2. A cubic function with 2 real roots.
3. A cubic function with only 1 real root.
Unit 16 Day 2 Polynomials
Find xintercepts and yintercepts and graph on your calculator to check
y = 0.5(x 3)(x 2)(x + 4)
y = 3(x 4)2 Convert to general form:
x int _______
y int _______
x int _______
y int _______
Convert to general form:
Identify the xintercepts and yintercept from each equationThen check on graphing calculator.
y = 2(x 1)(x + 1)(x 2)
x ints:
y int:
y = (x 3)(x + 2)2
x ints:
y int:
1, 1, 2 3, 2(Double)
(3)(2)2 = 12
(0, 12)
2(1)(1)(2) = 4
(0, 4)
erasable
Double Root Bounces
Unit 16 Day 2 Polynomials
Factor to find the x intercepts.
x2 16 x2 +16 (x 4)(x + 4)
Roots: 4 & 4
(x 4i)(x + 4i)
Roots: 4i & 4i
erasable
Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor)
4. Convert to general form:
1. Write equation using xintercepts
2. Plug in yintercept
3. Solve for "a"
y = __(x + 3)(x 4)
24 = a(3)(4) = 12a
a = 2y = 2(x + 3)(x 4)
review may skip for time
erasable
Unit 16 Day 2 Polynomials
Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor)
4. Convert to general form:
Write equation using xintercepts
Plug in yintercept (0, 2) & Solve for "a"
y = __(x + 4)(x + 1)(x 2)
2 = a(4)(1)(2) 2 = 8a.25 = a
y = .25(x + 4)(x + 1)(x 2)
erasable
OYO: On your own
Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor) Write equation using
xintercepts
Plug in yintercept & solve for "a"
4. Convert to general form:
SKIP Unless needed
may skip for time
erasable
y = __(x + 2.5)(x 3.2)(x 7.5)
90 = a(2.5)(3.2)(7.5)90 = 60aa = 1.5
y = 1.5(x + 2.5)(x 3.2)(x 7.5)
Unit 16 Day 2 Polynomials
Homework: WS #2 in GC
I can find the x,y intercepts of a polynomial equation
I can convert from factored to general form
I can solve for the scale factor of a polynomial
How are you doing?
Unit 16 Day 2 Polynomials