Graphing quadratic functions

Question

For the quadratic function (x)=-1/3(x+6)(x+6)+3, tell whether the graph opens up or down; wider or narrower; vertex and axis.

 

Ok so I think I have the idea for this

 

Vertex: (h,k)=(-6,3)

Axis: x=6

 

  X   /   Y

 -6     3

 -8     1.67

 -7     2.67

 -5     2.67

 -4     1.67

 

A=1 so the graph would open up

 

^^^I think that is all correct

but how do you determine if the graph is wider or narrower?

Answer 1

Actually, this parabola opens down, which you can tell from the negative sign in the -1/3 value - note that as x increases, y goes to a larger negative number (down). The width, you can tell from the 1/3 value. This parabola will be wider than the standard y= -x^2 parabola, because  the y-values increase more slowly (1/3 of the rate) for a change in x value.