Part 1: Write the general form of the equation which matches the graph below.
Part 2: In complete sentences, explain the process taken to find this equation.

Question

Part 1: Write the general form of the equation which matches the graph below. 
Part 2: In complete sentences, explain the process taken to find this equation.

anonymous · Answer

attachment

valpey · Answer

This is a parabola. Parabolas are defined as the set of points which are the same distance from some focus as the are from some line. In this case the line is x=3.5 and the focus is (-4,3).

valpey · Answer

*as they are

anonymous · Answer

so how would i make that in general form?

valpey · Answer

I'm sure there is an elegant version of this, but from first principles I would set the distance from (x,y) to A equal to the distance from (x,y) to the line.
$$\sqrt{(x-a_1)^2+(y-a_2)^2}=|x-3.5|$$

valpey · Answer

I mean:
$$\sqrt{(x-a_1)^2+(y-a_2)^2}=|x-l|$$

valpey · Answer

Oh, and I just noticed the line isn't x=3.5, it is x=4. Sorry.

valpey · Answer

Also, |x-l| is the absolute value of x-l if that wasn't clear.

anonymous · Answer

okay, thank you

anonymous · Answer

wait so since its x=4 does the focus change?

valpey · Answer

The focus (A) appears to be at (-4,3).

valpey · Answer

So for instance, the point (-4,11) is on the line because the distance from (-4,11) to the focus is 8 and the shortest distance from (-4,11) to the line x = 4 is also 8.