Pre-Algebra: Chapter 8-4
Equations as Functions
Functions are described as f(x) = 3x + 4. Instead of y = 3x + 4, functions have x on both sides of the equation, but the f(x) is nothing more than y. Also, instead of setting y to 0, 1, or 2, we set f(x) to the domain {0, 1, 2} with squiggly brackets showing the differences. This way of writing these equations is called FUNCTIONAL NOTATION, just to confuse you some more!
For example, if we have g(x) = 3x + 4, find g(3) by plugging in 3 wherever you see an x. Therefore, g(3) = 3 * 3 + 4 (remember PEMDAS) for answer of g(x) = 13. Another example, 2g(0) would equal 2 *[3 * 0 + 4] which becomes 2g(0) = 8.
Remember, the vertical line test to determine if these are functions as well.
Algebra: Chapter 6-3
Trinomial Squares
We are going backward again, using the properties:
- (a + b) * (a + b) = a^2 + 2ab + b^2 = (a + b)^2
- (a – b) * (a – b) = a^2 – 2ab + b^2 = (a – b)^2
For a trinomial square to factor, we must make sure that:
- 2 of the terms must be squares, a^2 and b^2
- There must be NO MINUS sign before the a^2 and b^2
- If we multiply a and b and double the result, we get the 3rd term, 2ab or its additive inverse – 2ab.
Sometimes, we can also factor out a coefficient in front of the a^2, like 2a^. We MIGHT be able to factor out the 2 before we start the trinomial determination.
Here is a purplemath link that describes trinomial squares, scroll down about 1/2 way to get to the information.