# Week 8 Pre-Calculus 11

This week in Pre-calculus 11 we were reviewing what we did before the spring break and we were introduced to graphing quadratic formulas. The main point of this week was transforming the graph of $y=x^2$.

The Are 3 possible equations you can use:

$y=x^2+q$

$y=(x-p)^2$

$y=ax^2$

The first formula adds q to the parent function which was listed first, this decides the Y-Intercept and so the parent either goes up or down when it is implemented.

The Second one changes the X-Intercept and changes the parabola location from side to side if p is being subtracted from the parabola the intercept moves right and the opposite happens when added.

The third function decides how wide or how skinny a parabola is, the higher the number the skinnier the shape. But if the number is smaller parabola will get wider. If ‘a’ is negative it reflects just like any function.

Below I will show examples for each of the 3 functions you can use. Please take into consideration how the parabola transforms.

$y=x^2+2$

As you can see the blue line is the principle function but when the 2 is added the line transforms 2 spaces up

$y= (x-4)^2$

As you can see parabola moves over to the right 4 spaces because the q value was negative.

$y=2x^2$ and $0.5x^2$, in this example there are two variations. The 2 is represented in green and the decimal is represented by the color blue.

As you can see the smaller number is the wider the parabola gets (blue line) but as the value of “a” gets larger the parabola gets skinnier.