# Week 6 – Precalc 11

For week 6 of precalc 11, we used the acronym we used last week to start our unit in solving Quadratics. We had a small lesson (3.1) on factoring polynomials which were mostly review. Starting lesson 3.2 all the way to 3.4 were newly learned concepts about Quadratic equations.

In 3.2 we learned that firstly, linear equations only ever have 1 solution, but if the equation is quadratic, meaning it was a degree of 2 (or a square exponent), there could be 2 solutions.

Using the formula: Ax2 + Bx + C = 0, techniques like the zero product law and isolating variables are used in polynomials to find the values of x.

In Lesson 3.3 we learned how to use square roots to solve Quadratic equations. Concepts like perfect square trinomials were learned. Chopping “B” in half and squaring it is how to find “C” in a perfect square trinomial.

In the most important lesson 3.4, we learned how to develop and apply the Quadratic formula.

There were two ways to solve Quadratic equations. First was the perfect square method :

Example :

2x2 – 12x + 5 = 0

= 2(x2 – 6x) + 5 = 0

= 2(x2 – 6x + 99) + 5 = 0

Take the perfect square trinomial now 2(x2 – 6x + 9) and multiply the -9 out of the bracket by 2 turning it into -18

= 2(x – 3)2 – 18 + 5 = 0

= 2(x – 3)2 – 13 = 0

= 2/2(x – 3)2 = 13/2

Then square root the (x – 3)2 and the 13/2 giving you the variable x – 3 by itself

Move -3 to the right side and the answer is

= x = 3 +- $\sqrt{26}$/2

The other method uses the Quadtratic formula where you simply input all the variables you know and solve: