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By : Ana Cristina Andrade

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

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By : Ana Cristina Andrade

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  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:

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