# Precalc week 8

This week in Precalc we continued with quadratic functions and analysing them to be able to graph them and how to use information given to interpret the equation to be able to graph it.

We started the week with a skills check.  When trying to graph an equation, you can look for clue in the equation that will indicate what quadrant the parabola is located in.  I learned that the function $y=x^2-5$ means that the parabola will be below 0 so near the bottom of the graph opening up.  When the function is $y=(x-3)^2$ it means the parabola will be in quadrant 1 and moved 3 units to the right.

In lesson 4.4, when learned how to analyse $y=a(x-p)^2+q$.  If $|a| \textgreater 1$, then it’s a stretch.  If $|a| \textless 1$ then its compressing.

We also learned that if you complete the square of a function, you will find the vertex.

Ex :

$y=x^2+8x+2$

$y=(x+4)^2-14$

Vertex = (-4, -14)

We also know that if provided with certain information about a graph, we can determine a variable such as A.

Ex :

Vertex : (-5, 2)

Y-int : -8

$-8=a(0+5)^2+2$

$-8 =25a+2$

$\frac{-2}{5} = a$

$y = \frac{-2}{5}(x+5)^2+2$