# Math 11 PreCalc, Week 8

This week in math we started a new unit called analyzing quadratic functions, it’s mostly graphing which isn’t too hard but since this was the first week back from spring break it took me a little to get back into the groove of things. so something we learned this week was how to analyze $y=a(x-p)^{2}+q$ . So first you need to know about a graph and the shape that it makes when a graph has an equation like this, the shape it makes is like a U that can change as the numbers or the signs change. Let’s start with the A, the is for stretch or compression so if the U shape is skinny or wide on the graph, the P tells us the horizontal translation so if it was positive it would be left and negative would be right, and finally the q which tells us if the U is facing up or down positive meaning its like a normal U and negative means its upside down. so for an example question with this equation $y=(x-1)^{2}+2$ would have the U going one to the right and two to the left it and it would open up. it seems pretty easy but it gets more and more complicated the more you need to remember about how to analyze the specific equations that lead into the graphs.