Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Thursday, October 24, 2013

Solving Equations Quadratic in Form

In this section, we make use of all the techniques that we have learned so far for solving quadratic equations. In fact, the equations found here are reducible to quadratic form.
Here are most of the reducible equations that we are likely to encounter. Begin by trying to identify what can be squared to obtain the leading variable term.
Tip: Look at the middle term for a hint as to what u should be.
In the previous solved problem, we certainly could have distributed the expression on the left side, put the equation in standard form then re-factored it. Instead, here we are illustrating a technique that will be used to easily solve many other equations that are quadratic in form.

Solve by making a u-substitution.

Solve: x^6 + 26x^3 -27
Six Answers: { -3, 1, (3±3iSqrt(3))/2, (-1±iSqrt(3))/2 }

So far we have been able to factor after we make the u-substitution.  If the resulting quadratic equation does not factor, then use the quadratic formula.
YouTube Videos:


Wednesday, October 23, 2013

Logarithms, Exponentials, and Equations

Notes and video examples covering the following topics:

Function Composition:
Inverse Functions:
Exponential Functions and Their Graphs
The Natural Exponential Function
Logarithmic Functions
Graphing Logarithmic Functions

Change of Base Formula
Properties of the Logarithm
Solving Exponential Equations
Solving Logarithmic Equations
Compound Interest Problems

Exponential Growth and Decay