In this unit, we built upon what we learned in the previous unit about quadratic equations and learned how to analyse these equations on graphs, how to model quadratic equations on graphs, and how to interpret those graphs.

My lifeline this unit has been the following key:

General form: $y=ax^2+bx+c$

Standard form: $y=a(x-p)^2+q$

To convert between general form and standard form, complete the square (we learned how to do this in Unit 3.)

a:

• a > 1 = vertical expansion (becomes thinner)
• 0<a<1 = vertical compression (becomes wider)
• a>0 = minimum value (open up)
• a<0 = maximum value (open down)

p:

• p>0 = horizontal translation to the right
• p<0 = horizontal translation to the left
• p determines the x value of the vertex and the axis of symmetry

q:

• q>0 = vertical translation up
• p<0 = vertical translation down
• p determines the y value of the vertex.

# Math 11 Sequences and Series Blog Post

Arithmetic
General Term: $t_{n} = a + (n-1)d$
To figure out the value of any given term ($t_{n}$), a (the first term), d (the common difference), or n (the term in which a certain value appears).
Sum of Terms: $s_{n} = [(a+t_{n})n]\div2$
To figure out the sum of any given arithmetic series ($S_{n}$), n (the last term), or a (the first term).

Geometric
General Term: $t_{n} = ar^{n-1}$
To figure out any given term ($t_{n}$), a (the first term), r (the common ratio), or n (the term in which a certain value appears).
Sum of Terms: $S_{n} = [a(r^n-1)]\div (r-1)$
To figure out the partial sum of any geometric series if not given the last term, the last term, the first term, or the common ratio OR
$S_{n} = (rt_{n} - a)\div (r-1)$
to do the same thing, but if given the last term of the series.

You can have two types of geometric series: convergent (terms come closer together) or divergent (terms become further apart).
When you have a convergent series, the common ratio is greater than -1 but smaller than 1 (and cannot equal zero). Convergent series have infinite sums (the number in which the sum of all the terms converge at), which can be calculated with the formula $S_{\infty} = a\div (1-r)$.
Divergent series don’t have infinite sums.