Math Reflection 2

1. The area of a rectangle can illustrate the distributive property in several ways. First, one side of the rectangle could be broken up into different segments and the other sides value ( such as x) could me multiplied by the addition of the different segments. Also, both sides could be divided into different segments and the addition of the segments of one side could be distributed on the addition of the segments of the other side.

2.a. If a quadratic expression is in factored form you can change it to factored form by distributing one of the segments on the addition of the other side's segments, and then distributing the other segment on the combination of the other side.

2.b. You change a quadratic expression which is in expanded form to an expression in factored form by first figuring out which two numbers divide the variable by so that the addition of both numbers adds up to what it was originally was and can multiply to get the number in parentheses. For instance 6x+9=3x+3x+9. The next step is to find the common number or variable that go into each segment and multiply it by the segments of that side divided by that specific number or variable and add it to the same thing for the other side. For instance 3x+6=3(x+2) The final step is to distribute it so that each set of parentheses have both a variable and a number and the the parentheses are multiplied by each other.

3. You know that an equation in factored form is quadratic if the highest exponent is exactly 2. You know that an equation in expanded form is quadratic if it has 2 variables both raised to the first power.

4. The shape of a graph of a quadratic expression is always a parabola. This means that it looks like a hill or and upside down hill. If it opens down the slope starts high and gets smaller as x gets higher until the slope becomes negative and changes direction the negative slope increasing. It is the other way around for a slope that opens up. The graph also usually has two x intercepts unless the x intercept is the graphs max point (for a graph that opens down) or the x intercept is the minimum point (for a graph that opens up). Finally, the graph of a quadratic equation is symmetrical mirroring it self once it hits its max or minimum point.