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.