Graphing Parabolas

Question

For the following quadratic functions, state the transformations that have occurred to the parent function, state the vertex and whether the parabola will open up or down and sketch the curve by hand. 

y = -2x^2

y = 1/3 x^2

Answer 1

I can't tell from the posting exactly what your question about the problem is, but maybe these pointers will help.

"Parent function" just means the most basic version of the equation / function. In this case, that's y=x^2

When you change that to y=ax^2, here's what happens:

If a>1, the parabola gets skinnier (because every time the y value goes up, it's going up by even more)

If 0<a<1, the parabola gets wider (because every time the y value goes up, it's only going up a fraction of what it does in the parent function)

If a<0, the parabola flips upside down (and you can replace "a>1" with "a<-1" and so on in the previous two lines)

Hope this helps!