1 / 19

By : Ana Cristina Andrade

Quadratics Journal. By : Ana Cristina Andrade. What is a quadratic function ?. What is a Quadratic function ?

freira
Download Presentation

By : Ana Cristina Andrade

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. QuadraticsJournal By: Ana Cristina Andrade

  2. Whatis a quadratic function? Whatis a Quadraticfunction? A Quadraticfunctionis a functionthat has theform y=ax²+bx+c. Whenitisgrapheditis a parabola. Theparabola can beuprightorupsidedowndependingonthesing of “a”. It can alsobewiderorskinerdependingontheabsolutevalueof “a”

  3. Quadratic and linear functions:

  4. Examples: Linear: Quadratics: Y= 2x-7 Y= 9x-8 Y=-10x-5 Y= 3x²+2x-7 Y= 7x²-9x-8 Y=-2x²+10x-5

  5. Graphingquadraticfunctions: Tographquadricfunctionsyou use : y=a(x-b)²+c • C: • Movesvertex up ordownC units • positive goes up • Negativegoesdown Less than 0 • B: • Movesvertexleftorright B units • Positive – left • Negative - right • A: • Less than 0 – Goesdown (like a rainbow) • More than 0- Goes up (like a horseshoe). • Greater than 1 – skinier • Less than 1 - wider More than 0

  6. Maximum and minimum Whentheparabola opens up, it has a minimumvalue at thevertexand whenit opens downit has a maximumvalue at thevertex.

  7. Parabola

  8. Examples:

  9. Solvingquadraticequations Bygraphing • STEPS: • GRAPH THE FUNCTION • IDENTIFY A, B AND C • CALCULATE BY USING –B/(2 A) BY PLUGGING IN THE NUMBERS. • USE T-TABLE TO GRAPH • FIND X-INTERCEPT(S) ON THE GRAPH • YOUR SOLUTIONS ARE THE X-INTERCEPTS.

  10. EXAMPLES:

  11. Solvingquadraticequations Bysquareroots Leave X² alone Findthesquareroot of thenumbers Iftheone of thenumbersorthenumber has no exactsquareroot, then factor thenumber and findthesquareroot of oneorboth of thoesnumbers. Thenwriteplussminusinfrontthenumber.

  12. EXAMPLES:

  13. Solvingquadraticequations usingfactoring: STEPS: WRITE THE EQUATION IN STANDARD FORM FIND GCF CANCEL GRATEST COMMON FACTOR BY DIVIDING THAT NUMBER ON BOTH SIDES FACTOR THE TRINOMIAL EQUAL EACH FACTOR TO 0 SOLVE EACH LINEAR EQUATION

  14. Examples:

  15. Solvingquadraticequations Usingcompletingthesquare: Steps: Thecoeficient of X² mustbe =1 Isolate C Complete thesquare Add(b/2)² tobothsides Write as a binomialsquared. Solvebyusingsquarerootbothsides Dontforgetthe +- (plussminus) Isolatethe variable

  16. Examples:

  17. Solvingquadraticsusing Thequadratic formula: Steps: Write in standardformyourequation. Find a, b, c Plug them in the formula solve TheQuadratic Formula:

  18. Discriminant in thequadratic formula Tosolve a quadraticeqationwe can firstcalculatethediscriminantto determine number of solutions. Ifthediscriminantis positive, theequation has twosolutions. Ifitis 0 it has onesolution. Ifitisnegative, thentheequation has no real solution.

  19. Examples:

More Related