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Chapter 6 - Exploring Quadratic Functions and Inequalities


"Focus of a Parabola" Java Program
Manipula Math's Java Program "Focus of a Parabola" lets you see how the parallel rays meet at the focus and how they are affected by the shape of the parabola. You adjust the leading coefficient to change the shape of the parabola. (click here).


"Drawing a Parabola" Java Program
Manipula Math's Java Program "Drawing a Parabola" lets you draw the points that meet the definition of a parabola: the loci of points equidistant from a point (the focus) and a line (the directrix). (click here).


Triangular Numbers (reference problem 55, page 374)
Note the definition of "figurate numbers" - sets of numbers that can be represented by shapes. Other examples: square numbers, pentagonal numbers. These sets of numbers are recursive, the next number in sequence can be found from the preceding number. This means you need a starting number in the set which for triangular numbers is one (1). Of course one point does not make a triangle, but neither do three or six or nine points since a triangle is formed of three line segments, each of which has an infinite number of points. The set of numbers and the formula to generate the set of numbers that we call "triangular numbers" appear in many problems that have nothing to do with actual geometric triangles. Bonus question, how do triangular numbers relate to the problem Gauss solved as a child in his first math class. The one we discussed in class where he handed in his slate after a brief time while the rest of the class tried to add all the numbers. And Gauss was the only one to get it right! Another bonus question, what is the definition of a "palindrome"? How about a palindrome number? How about a palindrome triangular number?



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