Math Reflection 2

1) The area of a rectangle can illustrate the Distributive Property. For example, if you had a square with lengths x and you add 3 to one side and subtract 2 from the other side your equation would be A=(x+3)(x-2). If you change the rectangle at all it can be shown in the equation. If you double one side the equation would be A=2x(x). No matter how you change it you will be able to recognize the difference in the equation with Distributive Property.
2a) If a quadratic expression is in factored form, to find an equivalent expression in expanded form all you have to do is do it out using distributive property. For instance, the equation in factored form is A=x(x+7)-5. You would do A=(x(x)+x(7))-5. After that the equation is A=x^2+7x-5, and that is the equation in expanded form.
2b) If a quadratic expression is in expanded form, to find and equivalent expression in factored form you use distributive property backwards. First you the common variable, then you put that out of the parentheses and put the other numbers or variables divided by the common factor in the parentheses and you have your equation. For example, the expanded equation is A=X^2-4x. The common variable is x. X^2/x=x, -4x/x=-4. You now have the numbers and variables that go inside and outside of the parentheses. The final equation is A=x(x-4).
3) You can recognize a quadratic function from its equation because in expanded form there will be a variable squared, or in factored form there will be a variable times itself.
4) The shape of a graph of a quadratic function is a parabola. It is u-shaped or upside down u-shaped. There are no straight lines and there are maximum and minimum points. There are two x-intercepts, and one y-intercept. There are also lines of symmetry whose equations usually equal x=x coordinate of maximum/minimum points.