MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.8.htm © 2025   A2, Agnes Azzolino (line)(line)= (quadratic), (Polynomial)(polynomial) = (polynomial) Quadratic & other Polynomial Functions, Text 5.1,5.2, 5.3,5.4,5.5, PG.375, 393, 402

Welcome to Precalc! Think Multiplication of Linear & Higher Order Factors Hi,     It is true that a (line)(line)= (quadratic).     It is true that a (Polynomial)(polynomial) = (a higher order polynomial).     Contact me through the pink box on www.mathnstuff.com/math/math.htm or with the phone number on your class CANVAS home page.     Stay safe, A2

5.1 - Quadratic Functions, pg. 344 (see day 2) 
	* Recognize characteristics of parabolas.
	* Understand how the graph of a parabola is related to its quadratic function.
	* Determine a quadratic function’s minimum or maximum value.
	* Solve problems involving a quadratic function’s minimum or maximum value.
5.2  - Power Functions and Polynomial Functions, pg. 360
	* Identify power functions.
	* Identify end behavior of power functions.
	* Identify polynomial functions.
	* Identify the degree and leading coefficient of polynomial functions.
5.3  - pg 375
	* Recognize characteristics of graphs of
	* Use factoring to find zeros of polynom
	* Identify zeros and their multiplicities.
	* Determine end behavior.
	* Understand the relationship between d
	* Graph polynomial functions.
	* Use the Intermediate Value Theorem.
5.4  - pg 393
	* Use long division to divide polynomials.
	* Use synthetic division to divide polynomials.
5.5  - pg 402
	* Evaluate a polynomial using the Remainder Theorem.
	* Use the Factor Theorem to solve a polynomial equation.
	* Use the Rational Zero Theorem to find rational zeros.
	* Find zeros of a polynomial function.
	* Use the Linear Factorization Theorem to find polynomials wi
	* Use Decartes' Rule of Signs.
	* Solve real-world applications of polynomial equations.
5.7 - pg 435
	* Find the inverse of an invertible polynomial function.
	* Restrict the domain to find the inverse of a polynomial function.

Visit the Interactive Sketch Pad Material On This Topic Polynomial and Rational Functions compositeFX.gsp -- compositeFx.poly.ratl.gsp 0 - graph of 1 function 1 - graphs of 2 functions 2 - composite of 4 functions 3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant 4 - rational, rational function features & how to find them 5 - end behavior, battle of (Ax^m)/(Bx^n) parabola.gsp   -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,     * both generated by equations defined by parameters.     * WITH SHOW/HIDE ACTION BUTTON     * graphs of 2 parabolas: 1 in general form, 1 in standard forms,     * 1 parabola, set a, then generat parabola w/2 points.     * 1 parabola controlled by 3 points, used for determinant analysis     * 1 vertical axis of symmetry, 1 horizontal "axis of symmetry" TracePoly   -- drag point f(x) to state and show new ( x, f(x)) recipfx   -- graph of parameter-defined reciprocal function,     * with slide-able tangent line,     * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER! line.gsp   -- slide points A and B and generate equation of the line in 4 forms.

Spread Sheets -- Dynamic Computation polynomial spreadsheet --     graph a polynomial function written in factored form     complete synthetic division synthetic division spreadsheet -- just complete synthetic division of a polynomial or of a quadratic by a linear binomial rational function spread sheet     Graph and table of (Axm)/(Bxn)     Watch the power of the top or bottom equal or dominate the other.     Examine hoirzontal asymptotes or infinite increase or decrease.     Think endbehavior and explore.     Graph and table of rational function, polynomial A(x) divided by B(x).     Examine asymptotes.     Examine the role of factors A(x) and 1/B(x).     Graph and table of rational functions written as A(x) / B(x) + C(x)     Really play with C(x), the asymptote     Complete synthetic division and rewrite of quotient and remainder.