Algebra How to Factor Second Degree Polynomials (Quadratic Equations) If you have a fairly simple polynomial, you might be able to figure out the factors yourself just from sight. For instance, after practice, many mathematicians are able to know that the expression 4x2 + 4x + 1 has the factors (2x + 1) and (2x + 1) just from having seen it so much. (This will obviously not be as easy with more complicated polynomials.) For this example, let's use a less common expression: 3x2 + 2x - 8 1List the factors of the a term and the c term. 9Double-check your signs if necessary. Δημήτριος Ζαχαριάδης Σας περιμένουμε στη νέα διεύθυνση: blogs.sch.gr/dyoin/ Τελευταία δημοσίευση Το blog που βλέπετε δημιουργήθηκε στον Οκτώβρη του 2010 όταν ανέλαβα σχολικός Σύμβουλος του Νομού Λέσβου. Σκοπός του ήταν να αναρτηθούν δειγματικές διδασκαλίες που θα πραγματοποιούνταν στα σχολεία του νομού μέσα σε εκείνη τη σχολική χρονιά. Παρ” όλες τις δυσκολίες που παρουσιάζει η οργάνωση και παρουσίαση μιας διδασκαλίας, υπήρξε ενθουσιασμός από τους συναδέλφους του νομού και εθελοντική προσφορά στο έργο αυτό. Εκτός από τις διδασκαλίες έγινε δημοσίευση με την σύμφωνη γνώμη των συναδέλφων, ενός μεγάλου αριθμού διαγωνισμάτων και θεμάτων εξετάσεων που διενεργήθηκαν σε σχολεία της Λέσβου της Λήμνου και του Αγίου Ευστρατίου. Καρπός της δουλειάς που κάναμε με του συναδέλφους της Λέσβου τη χρονιά εκείνη ήταν και τα βιντεομαθήματα για το πρόγραμμα Geogebra που δημοσιεύτηκαν επίσης στο blog. Δημήτρης Ζαχαριάδης επ.
Algebra Worksheet Generator Select number of each type of equations: One-step Equations: (e.g.. x-4=10) Two-step Equations: (e.g.. 2x+6=16) Combining Like Terms X's on both sides Distributive Property Systems - solve for x and y solve by adding solve by subtracting a mix of the above two require one multiplication step general system solve by substitution Quadratics - ax2+bx+c=0 simple factorable difficult factorable (a not equal 1) general - require quadratic formula imaginary solutions, general Note: There will be no ads on the worksheet. Options: Create Answer Sheet also Include Header No Negatives Percent of coefficients that are fractions Printing tips - For best printed results. Permissions - Can you photocopy these worksheets? Answer sheet pops up in separate window.
Graphing Quadratic Functions: The Leading Coefficient / The Vertex Graphing Quadratic Functions: The Leading Coefficient / The Vertex (page 2 of 4) Sections: Introduction, The meaning of the leading coefficient / The vertex, Examples The general form of a quadratic is "y = ax2 + bx + c". For graphing, the leading coefficient "a" indicates how "fat" or how "skinny" the parabola will be. For | a | > 1 (such as a = 3 or a = –4), the parabola will be "skinny", because it grows more quickly (three times as fast or four times as fast, respectively, in the case of our sample values of a). For | a | < 1 (such as a = 1/3 or a = –1/4 ), the parabola will be "fat", because it grows more slowly (one-third as fast or one-fourth as fast, respectively, in the examples). There is a simple, if slightly "dumb", way to remember the difference between right-side-up parabolas and upside-down parabolas: Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). Find the vertex of y = 3x2 + x – 2 and graph the parabola.
Secret Worlds: The Universe Within - Interactive Java Tutorial Secret Worlds: The Universe Within View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons. Once the tutorial has completely downloaded, a set of the arrows will appear that allow the user to increase or decrease the view magnitude in Manual mode. Click on the Auto button to return to the Automatic mode. Notice how each picture is actually an image of something that is 10 times bigger or smaller than the one preceding or following it. Earth = 12.76 x 10+6 = 12,760,000 meters wide (12.76 million meters) Contributing Authors David A. Questions or comments?