Graphs on Cartesian plane

May 2013
Hi guys,

This is grade 11 algebra.

The task is: Image #192480 - Image Hosting (pasted image), or in writing: Draw each of the graphs on the Cartesian plane below. Clearly show the symmetry axis, the coordinates of the turning point and the y-intercept on these graphs.

f(x) = 2x^2
g(x) = 2(x-2)^2
h(x) - 2x^2-2
k(x) = 2(x+2)^2
m(x) = 2x^2+2

Then, "explain in words what happened to f to form g, h, k, and m".

I'm not too sure about either section, but I can probably figure out the first part. If I'm not mistaken, it's just u-shaped parabolas. I have no idea what the written explanation should be though. My teacher isn't much use so any help will be appreciated. :)
Dec 2011
St. Augustine, FL.
Basically, the graph of \(\displaystyle y=a(x-h)^2+k\) is the graph of \(\displaystyle y=ax^2\) shifted \(\displaystyle h\) units to the right and \(\displaystyle h\) units up.

The vertex (turning point) of \(\displaystyle y=a(x-h)^2+k\) is the point \(\displaystyle (h,k)\), the axis of symmetry is \(\displaystyle x=h\) and the \(\displaystyle y\)-intercept is found by letting \(\displaystyle x=0\) to get the point \(\displaystyle (0,ah^2+k)\).

Can you proceed?