Algebra: Chapter 6, Lesson 8, page 286.
Solving Equations by Factoring
The principle of zero products states that: for any rational numbers a and b, if the product `ab = 0`, then `a=0` or `b=0` or both `a` and `b = 0`.
Factor and solve equations by using the following:
- Get `0` on one side of the equation using the addition property
- FACTOR the expression on the other side of the equation
- Set each factor equal to zero
- Solve each equation.
If we have an equation with `0` on one side and a factorization on the other side, we can solve the equation by finding the values that make the factors `0`. This is even easier!
Since we are solving quadratic equations (they are NOT linear because they have an exponent that is squared, `x^2`), we can have at MOST 2 solutions. We can have NO solutions, 1 solution or 2 solutions.
Remember to use all the techniques you know to factor!
Two of tonight’s homework problems solved by MrE are here! Just click it!
======================================================================
Algebra 1a: Chapter 7, Lesson 7, page 333.
Fitting Equations to Data
“The mathematical relationship between 2 variables is of interest in many real-world situations. The relationship between 2 variables can often be expressed as a linear equation, which is calleda model of the situation. The model can be use to make estimates or predictions about the quantities represented by the variables.”
In the problems with real-world data, we sometimes have to approximate, by plotting the data on a x-y graph and then drawing (fitting) a line the best way we can through MOST of the data. We can then use 2 of the points on our line to use to develop our linear equation.
We can use either the slope-intercept equation (`y = mx + b`) or the point-slope equation [`y – y_1 = m(x – x_1)`] to develop our linear equation.
Two of tonight’s homework problems solved by MrE are here! Just click it!