Find the vertex, focus, and directrix of the parabola given by the following equation:
I get up to
I don't know how to finish this.
Don't do that!
Instead of factoring, complete the square.
First, since the standard form for a parabola is either or , your objective is to get it into that form- and that " should tell you that you want to get a "perfect square". First swap that y over to the other side of the equation:
becomes
Now, you should have learned that [tex](y+ a)^2= y^2+ 2ay+ a^2[/itex]. Compare that to " ". Clearly that has 2a= 8 so a= 4. Then : . To make a "perfect square" (complete the square) we must add (and subtract) 16.
so that, finally, .
Okay, what does that "standard form" tell you about "vertex", "focus", and "directrix"?
Now, look at the formulas in your book. What does