Week 9 – Math 11

This week in math 11 we learned how to change an equation from one form to another to find information we need for graphing. The three different forms of an equation are Vertex/Standard from, General Form and Factored Form. The way you change them is by using formulas that we have been using to awhile now, completing the square, and factoring.

If you were given an equation in General Form an were asked to change it to Vertex Form you would use completing the square. If the equation was first you would divide by -4 to get the by itself, then you will re-write your equation as . In order to find the numbers that go in the blank you will need to divide the 6 by 2 then square it. That would give you 9, you then put the 9 in the 2 blank spots. Your equation will now be . 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 . The next step is to subtract the 7 from 36 leaving you with 29. Your new equation is .

With this 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. Before with the equation only in general form all we are able to find is the Y-Intercept, this is still a useful point to have but won’t help us much if that is all the information we have. The other form is acted from and from that form you are able to gather X-Intercepts (roots) of the parabola.