x^2 + 5x - 4y -1 = 0?

Question

The instructions are find the vertex, focus, and directrix of the parabola given by each equation and sketch the graph. Anybody want to help me with this one. Also if anybody knows how do do the graphing with an older TI 82 that would help also.

Answer 1

This is a nasty problem. Anyway, since this is a parabola you can either use -b/2a to get the vertex or complete the square. The equation would be (x+5/2)^2=4(y+29/16) so the vertex would be (-5/2, -29/16). Since 4p=4, p=1 so the directrix would be y= -45/16. The focus would be (-5/2, -13/16).

There's probably an easier way to do conics on your calculator, but until you find that way here is what I'd suggest. Since it's a parabola with y to the first, just solve it for y, you get y=.25x^2+1.25x-.25, then graph it. If you have y^2 solve the equation for y^2 then square root both sides which will get you a positive and negative answer. Put the positive answer in Y= , then on the next line in Y= put the negative answer. It's actually 2 square root functions creating the parabola. I hope this helps.