# Week 9 – Precalculus 11

This week felt like a lot of review. Wether it be review for our chapter test tomorrow or our midterm on Thursday, it was packed with previous learning. At the start of the week we focused on going and working ‘between’ different equations and changing them from one form into another. The three forms we covered are General Form, Factored Form and Standard / Vertex Form. We can interchange these formulas to give us different pieces we need for graphing. Therefore, if you were given an equation in General Form and you were asked to change it to Vertex Form you would use the method of completing the square. If the equation was $y=-4x^2-24x-7$. First, you would divide by -4 to get the $x^2$ by itself, then you will re-write your equation as $y=-4(x^2+6+blank-blank)-7$. In order to find the numbers that go in the blank you will need to spilt the middle term and square it! (middle term being 6). That would give you 9, you then put the 9 in the 2 blank spots. Your equation will now be $y=-4(x^2+6+9-9)-7$. Next you will create your binomial and multiply the -9 by -4 to be able to move it to the outside of the brackets. Your new equation will now be $y=-4(x^2+3)+36-7$. The next step is to subtract the 7 from 36 leaving you with 29. Your new equation is $-4(x^2+3)+29$. With this new equation we are now able to find the vertex of the parabola, if it is positive or negative (opens up or down), and if it is congruent to the 1,3,5 pattern used when graphing.

Here is the same equation demonstrated on paper. 