Week 8 – Quadratic functions [y=x², y=a(x-p)² +q], and changes in various ways

A (not so) short summary of what I’ve learned about the changes of Quadratic functions this week:

On :

-any vertical translation of the graph is dependant on: (if q is a positive number, the graph moves up and vice versa)

-any horizontal translation of the graph is dependant on: (if p ends up being a positive/negative number, the graph moves to the left/right respectively, because this number is affected by a negative sign)

-determinating the width and reflection: (whereas if a is positive, it “opens up”, and “opens down” [reflection over the X axis] when a is negative. Any number, -1<a<1, will widen the graph and any a>1 or a<-1 will stretch the graph)

If two or more changes mentioned above were to be in a quadratic function, it will be changed into a standard form, 

For an example that I’ve made, , from this function, we know that the graph opens downwards (and it’s kinda stretched by a bit), a horizontal translation of 1 unit to the right (since p is now negative) and doesn’t have any vertical changes (since q is 0).