Question

Part 1: Write the general form of the equation which matches the graph below. (3 points)

Part 2: In complete sentences, explain the process taken to find this equation. (3 points)

http://assets.openstudy.com/updates/attachments/51faa5f3e4b0259e2c33a6c5-magbak-1375381008302-10_04g_29.gif

Answer 1

vertex is (0,+3)
directx is x=-4
f is on (4,3)

\[y^2=4px\\(y-y _{0})^2=4p(x-x _{0})\\p=4\\vertex\\is \\(0,+3)\\so\\(y-3)^2=4*4(x-0)\]

Answer 2

thank you !!!

Answer 3

Not to mention the DEFINITION - After finding the Focus.

Distance to Focus: \(\sqrt{(x-4)^{2} + (y-3)^{2}}\)

Distance to Directrix: \(x+4\)

Then a little algebra

\(\sqrt{(x-4)^{2} + (y-3)^{2}} = x+4\)

\((x-4)^{2} + (y-3)^{2} = (x+4)^{2}\)

\(x^{2} - 8x + 16 + (y-3)^{2} = x^{2} + 8x + 16\)

\((y-3)^{2} = 16x\)

\((y-3)^{2} = 4\cdot4\cdot x\)

Always keep your mind open to different approaches. Don't forget the ones you already know!