This week in precalc 11 we learned about the standard form aka Vertex form.

The standard form is the most useful form for finding graphs.

the formula is  y = a + q.

everything in the formula says something about the graph. Starting with a, a will usually tell you how thin or how wide a graph is. If there is no number there a = 1. And when a = 1 then we can see the width by following this: 1, 3, 5. those numbers show how far over you will go every time. so you go up 1 over 1 up 3 over 1 up 5 over 1 and you should hit the graph each time. but if a = 2 then you would go 2, 6, 10. Notice how when a is > than 1 the graph become longer and skinnier. when a becomes smaller it becomes wider.

the next important piece is p. P is sometimes difficult to understand. It determines if your graph slides to the left or right and is also the line of symmetry. so if you have and so 3 is your p variable then you would move 3 to the right. I know you see the negative and think you will be going left but you go just what p is if it was $latex (x – -3)^2 then you would move 3 to the left because p was -3.

now we have come to q. q determines where you are on the axis and this one doesn’t become weird like p with the negative in front you just put it wherever it says it is so if it’s -5 then you have the graph at -5.