# Graphs on Cartesian plane

#### maester

Hi guys,

This is grade 11 algebra.

The task is: Image #192480 - CtrlV.in 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.

#### MarkFL

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?