  Assignment 26

 "The theory of probability is at the bottom only common sense" -- (Pierre-Simon LaPlace, 1749-1827) The origin of some mathematical words. Isosceles: From the Greek words iso and skelos, meaning "equal legs." Integer: From the Latin word integer, meaning "perfect, whole, complete." Tangent: From the Latin word tangere, meaning "to touch." Trapezoid: From the Greek word trapeza, meaning "table." (Many tables today are trapezoid-shaped.) What did Herkimer say to Barbie, the play director, when the actor who was playing a chicken forgot his lines? Answer: "Barbie, cue the chicken." Things Herky would like to know: Why is it that no one is listening until you make a mistake? Should you fall behind in your homework early in the school year? This would give you more time to catch up. ASSIGNMENT #26 Reading: Section 5.2, pages 256-260. Exercises: Pages 261-262/65-83 (odds), 94, 95. Mathematical word analysis:SQUARE: This is derived from the Latin exquadrare, meaning "like a quadratic." The term was eventually contracted into its present form... square.

If a and b are real numbers, and ab = 0, then a = 0 or b = 0. In other words, if the product of two or more numbers is zero, then at least one of the numbers must be 0. This is an important real number property that can be used to solve quadratic equations. Remember: Factor means "write as a product." We can often solve equations using factoring.

Example:

x2 + 3x - 40 = 0

==> (x + 8)(x - 5) = 0

==> x + 8 = 0 or x - 5 = 0

==> x = -8 or x = 5.

Example:

x3 - 9x = 0

==> x(x2 - 9) = 0

==> x(x + 3)(x - 3) = 0

==> x = 0 or x + 3 = 0 or x - 3 = 0

==> x = 0 or x = -3 or x = 3.

Example:

Consider the parabola y = 3x2 - 12x - 15. If we want to find the x-intercepts, we want to know when y = 0. OK,

y = 0 ==> 3(x2 - 4x - 5) = 0

==> 3(x - 5)(x + 1) = 0

==> x - 5 = 0 or x + 1 = 0

==> x = 5 or x = -1.

The parabola intersects the x-axis at the points (5,0) and (-1,0).

 Problem: Solve the equation 2x2 + 4x - 1 = 7x2 - 7x + 1 Solution (with communication): 2x2 + 4x - 1 = 7x2 - 7x + 1 ==> 5x2 - 11x + 2 = 0 ==> (5x -1)(x - 2) = 0 ==> 5x - 1 =0 or x - 2 = 0 ==> x = 1/5 or x = 2. Problem: Find the zeros of the function y = 2x2 + 3x - 35 Solution (with communication): y =0 ==> 2x2 + 3x - 35 = 0 ==> (2x - 7)(x + 5) = 0 ==> 2x - 7 = 0 or x + 5 = 0 ==> x = 3.5 or x = -5. The graph passes through (3.5, 0) and (-5,0), so the zeros of the function are -5 and 3.5.