Quadratics 40 points A quadratic contains a squared variable (x2) as the highest-order term

Standard form: 2 y=ax +bx+c There can be 0, 1, or 2 solutions for x (also called roots)

Thats because solutions are where the graph of an 0 solutions 2 solutions

1 solution To solve: 1st: Always move everything to one side of the equation and set it equal to zero! 2nd: Use one of the following techniques...

OPTION 1: Factoring aka: reverse-FOIL This is ALWAYS easiest if a=1, so try to simplify your expression so that this is the case!

HINT: nice-looking numbers in answer choices= clue that factoring is possible For x2+bx+c: Look for the factors of c that add up to equal b For ax2+bx+c : multiply a times c, look for the factors of ac that add up to b, use those factors to break the middle term into two pieces, then factor by grouping Check your work by FOILing!

OPTION 2: Square Rooting: Use when both sides of equation are perfect squares OPTION 2: Square Rooting example:

Ex: (x+3)2 = 49 You can use the square root on both sides because both sides of the equation are perfect squares! (x+3) = 7

x= 4 OPTION 3: Completing the Square Use with more difficult quadratic equations 1st: put the quadratic in standard form

2nd: divide b by 2 and square the result 3rd: add the result to both sides of the equation, factor, & solve by square rooting Another example...

OPTION 4: The Quadratic Formula *Complicated math, so only use as a last resort! The Quadratic Formula Use to find an exact solution

HINT: Use when you see radicals in the answer choices! *Be sure to write in standard form before plugging in the values of a, b, and c into the formula! MEMORIZE this formula!!!! Discriminant: the sign dictates the # of REAL solutions of the equation

+ = 2 real solutions 0 = 1 real solution - = 0 real solutions You MUST solve the discriminant 1st!

Graphing Parabolas Note: Quadratics (& functions) graph as parabolas (U-shaped) When a<0: will open DOWN When a>0: will open UP *Be sure you are familiar with the terms on the image

ANOTHER way to see them: Vertex Form y = a(x - h) 2

+k h & k are the x- and - coordinates of the parabolas vertex, respectively, and the equation x = h give the axis of symmetry From standard form, plug in the values into x = -b 2a

This is the quadratic formula WITHOUT the square root part! To find the y-coordinate of the vertex, plug the x-coordinate into the original equation and solve for y!

Recently Viewed Presentations

  • Unit 5: Animals - Sponges, Cnidarians, &amp; Worms

    Unit 5: Animals - Sponges, Cnidarians, & Worms

    Sponges & Cnidarians (Section 24.3) Biology 102B Characteristics of Animals 1. Multicellular, eukaryotes 2. Heterotrophs 3. Cells w/out cell walls, many have specialized functions 4. Usually have a method of movement 5. Most reproduce sexually 6. Require oxygen Describe the...
  • Topic 1.2.3 - KESWICKSCHOOLPE

    Topic 1.2.3 - KESWICKSCHOOLPE

    ATP and CP can only supply energy for a short time so if the demand for energy continues for over a minute then the body uses carbohydrates to create energy. Lactic Acid / Oxygen Debt - Due to the absence...
  • Anxiety - University of Otago

    Anxiety - University of Otago

    Psychopharmacology of Anxiety Paul Glue ... 463:769-774 Anxiety and Histamine Antihistamines are effective anxiolytics Glutamate and Anxiety LY354740 in GAD Anxiety and Gabapentin/Pregabalin Pregabalin = Alprazolam > placebo in GAD Non-Pharmacological Treatments The future for anxiety drug ...
  • English 10 Honors Day 1 -

    English 10 Honors Day 1 -

    OPTIC Strategy. used to analyze visuals. process . O = overview . P= parts . T= title . I= Interrelatinships . C= conclusion . As we go over the grammar concepts, take notes. Be sure you understand how to identify...
  • WELCOME to Miss Belnap&#x27;s 3rd grade class!

    WELCOME to Miss Belnap's 3rd grade class!

    WELCOME to Mrs. Browning's 3rd grade class! Lunch is from 12:54-1:19 Special Area is from 9:35-10:20 Special Area Rotation Day 1 Art (Penn) Day 2 PE (Dunlap) Day 3 Music (Rhodes) Day 4 PE (Dunlap) Day 5 Media (Spearing) Day...


    ULTRA WIDEBAND (UWB) Wireless system with bandwidth more than 20% of carrier frequency or more than 0.5 GHz (defined by FCC) Evolved from Radar concept Very short duration pulses, typically less than 1 nsec UWB PROPERTIES Ultra wide Bandwidth High...
  • Introduction to Geocaching

    Introduction to Geocaching

    This screen shot is from a cache description. From there, it's very easy to find other caches nearby. Google maps and satellite images getting so good, sometimes you don't even need a GPSr! Programs such as GSAK and EasyGPS can...
  • Archetypes in Literature

    Archetypes in Literature

    Definition of Archetype. A recurrent character type, plot type, or symbol, which is identifiable in a wide variety of works of literature. It must cross cultural boundaries and time boundaries. An archetype is the first real example or prototype of...