MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.2.htm © 2025   A2, Agnes Azzolino Quadratics, Solving Equations Algebraically; Graphing functions, domain, range, etc. Text 2.5, 2.6, PG. 119, 137

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2.5 - Quadratic Equations, pg.  119, Learning Objectives
	* Solve quadratic equations by factoring.
	* Solve quadratic equations by the square root property.
	* Solve quadratic equations by completing the square.
	* Solve quadratic equations by using the quadratic formula.
2.6 -Other Types of Equations -- Solving Equations Algebraically, pg. 131,  Learning Objectives
	* Solve equations involving rational exponents.
	* Solve equations using factoring.
	* Solve radical equations.
	* Solve absolute value equations.
	* Solve other types of equations.

2.5 Quadratic Equations, pg. 119

• m129.ch2to4.1.fa24.pdf simplest radical form & computation from textbook, local only
• "Why = a(x - h)² + k?" -- EVERYTHING YOU EVER WANTED TO KNOW ABOUT A QUADRATICS BUT WERE AFRAID TO ASK
  Quadratics: In General (including equation formats), Solving Quadratics by multiple methods and in multiple formats,
  Graphing Quadratics, Uses of Quadratics
• The Quadratic Equation, Formula, & Discriminant
• solve using spreadsheet
• general to standard to general, as with abc (h,k) image
• quadr1.gsp experiment with a, b, c, and (h,k)
• quadratic
• quadratic formula
• discriminant
• Solve a Quadratic by Completeing the Square Instructions gif
• Squaring and Square Root Functions
• quadratic equation web page
• Uses of Quadratics:
        To Create Other Functions
        To Express Projectile Motion
  
• Image:   How the general equation y=ax² + bx + c and the standard equation y=a(x-h)² +k relate
• Game:   Oscar Reutersvard's Penrose Square -- Solve the quadratic. Connect the dots.               easy print pdf
• parabola sketchpad   -- 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 sketchpad   -- drag point f(x) to state and show new ( x, f(x))
• polynomial spreadsheet
      * graph polynomial function written in factored form
      * complete synthetic division computation
• quadratic spread sheet
      * enter a, b, c, get x1, x2, h, k
      * enter a, h, k, get x1, x2, a, b, c, and the discriminant
• Computes quadratic equation, formula, discriminant using a web page

2.6 Other Types of Equations -- Solving Equations Algebraically, pg. 131

            Calcu4: Solve an Equation w/Solver .gif (image)