Why area diagrams are important:
Creating area diagrams help you visualize the equations, and you are able to understand the problems better. Completing the squares help make the steps easier and clearer. |
Converting Between Forms:
For Vertex to standard you have to take the (x+3)^2 and do (x+3) two times next to each other because the ^2 tells us so. You bring down the -2, and , you multiply 3 times 3 and get 9. You combine the like terms to get (x^2 +6x+9)-2. You are left with two x's which you can write down as y=x^2+6x+7 Standard to vertex: To turn an equation from standard to vertex you take a out and group the ax^2 and bx together. By using the area diagram you fill out the missing numbers and subtract the added term. You take the subtracted term and multiply by a. Based on the square you rewrite the parenthesis and combine like terms. Factored to standard: You combine the like terms using the area diagram. For example, you would take the x+2 and put it on one side of the diagram, and do the same for x+4. You multiple the numbers and get 8. You then combine the x's and add 2+4, and 8 which we got from multiplying 2x4. Standard to factored: To convert standard to factored, you reverse and work backwards. You know that if p and q are added they equal the b constant. They have to be multiplied by values that equal to the a constant. You factor the a constant out. You would have to guess and check for the values. |