Minimum Point of a Quadratic Graph

Minimum Point of a Quadratic Graph

Differentiating the function and setting its derivative to 0 is the fastest way however if you do not know calculus then an alternate method is to complete the square. 

But for any quadratic in the form ax^2 + bx +c, where a, b and c are constants: the lowest point is when 

x = -b/2a.

The Rule of Four

The Rule of Four

Mathematics should be expressed in the following four ways:

1. Algebraically

2. Numerically

3. Graphically

4. Verbally

In order to understand mathematics holistically, it is important that students connect each concept with the rule of four.

Click Here

The beauty of this way of understanding mathematics is that it is so versatile; students can work with information presented in any one way and manipulate that information to find or interpret the information in other ways.

All students can learn

Three goals for the students:

1. Work accurately with basic operations:

2. Be able to apply basic operations to more complex problems.

3. Incorporate technology with the goal of higher level mathematics.

First and foremost my job is to ready my students for the next level of mathematics. Often, the level of mathematics dictates teaching methods.

When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.

When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.

"In order to understand Math, you must do Math."

Having too much fun with the graphing calculator!

"Understanding of math is more than following examples.  It is the conceptual 'why' and 'how' and being able to apply that."

"The Rule of Three: Every topic should be presented geometrically, numerically and algebraically."

Mathematics Worksheets

Mathematics Worksheets

• Math-Drills
• Math-Aids

Quadratic Equation Application '-Distance Speed Time

Quotes on Mathematics

Quotes on Mathematics

True beauty is a matter of maths

MATHEMATICS – The music of reason

As G H Hardy had aptly put it: “a mathematician, like a poet or a painter is a maker of patterns and that if his patterns are more permanent than theirs, it is because they are made with ideas.” 

Expectation and Fair price

Expectation and Fair price

A person spins the pointer and is awarded the amount indicated by the pointer. 



It costs $8 to play the game. Determine: 


· The expectation of a person who plays the game.


· The fair price to play the game.

My work:
E=P(wins)(amount won)+P(loss)(amount lost)
E=1/3(-6)+2/3(-8)
E=1/3*-6/1 + 2/3*-8/1
E=-2/1+-16/3
E=-6/3+-16/3
E=-22/3=7.333
E=$7.33

Fair price=expectation + cost of play
Fair price= 7.33 +8.00
Fair price= $15.33

This just doesn't seem right to me, can someone tell me where I went wrong?

Riemann integral

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of theintegral of a function on an interval.^[1] For many functions and practical applications, the Riemann integral can be evaluated by using the fundamental theorem of calculus or (approximately) by numerical integration.

The Riemann integral is unsuitable for many theoretical purposes. Some of the technical deficiencies in Riemann integration can be remedied with theRiemann–Stieltjes integral, and most disappear with the Lebesgue integral

The integral as the area of a region under a curve.

A sequence of Riemann sums over a regular partition of an interval. The number on top is the total area of the rectangles, which converges to the integral of the function.

The partition does not need to be regular, as shown here. The approximation works as long as the width of each subdivision tends to zero.

Average

In colloquial language average usually means the sum of a list of numbers divided by the size of the list, in other words the arithmetic mean. However it can alternatively mean the median, themode, or some other central or typical value. In statistics, these are all known as measures of central tendency.

Pythagorean means

The three most common averages are the Pythagorean means – the arithmetic mean, the geometric mean, and the harmonic mean.

Geometric mean can be thought of as the antilog of the arithmetic mean of the logs of the numbers.

Harmonic mean

reciprocal of the arithmetic mean of the reciprocals of the a_i's:

The mode has the advantage that it can be used with non-numerical data (e.g., red cars are most frequent), while other averages cannot.


Comparison of arithmetic mean, median and mode of twolog-normal distributions with different skewness.