MATH REFLECTION 2

1. The area of a rectangle demonstrates distributive property be multiplying the base by the height. Suppose you have a rectangle with a hieght of x and a base of x + 7. You gat the equation x(x+7). In order to solve this equation you need to distribute and multiply x by x and x by 7. After solving you get x squared + 7x.

2a. When turning quadratic equations from factored to expanded you can use distributive property. The equation (x+3)(x+5) is in factored form. Now to turn it into expanded you will distribute the (x+3) to (x+5). First multiply x(x+5) and then add 3(x+5). You will get x squared +8x +15.

b. When changing expanded form of quadratic equations to the factored form you can use+distributive property. The normal format for an expanded equation is x squared + yx + z. The two numbers that add up to y must also multiply to equal z. Now knowing this you can change x squared + 5x +4. You must find the two numbers that add up to 5 (y) and that also multiply out to equal 4 (z). Once you have found these you take the two numbers and write the equation again but instead of writing y you write ax + bx (a and b are the two number that add up to y and multiply out to z). x squared + x + 4x + 4. You will then distribute one of the x's in x squared to (x+1) and the 4 in 4x and distribute it to (x+1).

3. You can tell whether and equation is quadratic by looking to see if there are any variables that are squared or if there are any of the same variables being multiplied together.

4. Quadratic graphs are parabolas which are lines that look like arches or U's. There will most likely be two x intercepts if the line crosses the x axis. The x intercepts are given to you in the equation, especially if the equation is in factored form. If your equation is y=(x=5)(x-3) your x intercepts are 5,0 and -3,0. The y intercepts is the number that is directly between the two x intercepts. So in this situation it is 0, 1.

Nic S., Joe P., Mike K., and Harry K.