An extraordinarily quick way to sketch quadratics

Students in an algebra class spend many a week learning to sketch graphs of
quadratic functions:

y = ax2 + bx + c

And students are usually taught to memorise the following:

The graph is an upward or downward U-shaped graph (called a parabola)
depending on whether the leading coefficient a is positive or negative.

And the vertex of the parabola occurs at:   x = – (b/2a)

Plugging in this value of x into gives the y-coordinate of the vertex and plugging in other values of x will help ascertain the correct “steepness” of the U-shape.

My first piece of advice: FORGET THE FORMULA FOR THE VERTEX!  

Memorising is joyless!

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An extraordinarily quick way to sketch quadratics


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


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