SOLUTION: convert the equation to standard form by completing the square on x or y. then find the vertex, focus, and directrix of the parabola. finally, graph the parabola x^2+14x-12y+13=

Algebra ->  Trigonometry-basics -> SOLUTION: convert the equation to standard form by completing the square on x or y. then find the vertex, focus, and directrix of the parabola. finally, graph the parabola x^2+14x-12y+13=      Log On


   

Question 1089165: convert the equation to standard form by completing the square on x or y. then find the vertex, focus, and directrix of the parabola. finally, graph the parabola
x^2+14x-12y+13=0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
-12y=-x%5E2-14x-13
12y=x%5E2%2B14x%2B13
12y-13=x%5E2%2B14x
12y-13%2B49=x%5E2%2B14x%2B49
12y%2B36=%28x%2B7%29%5E2
highlight%2812%28y%2B3%29=%28x%2B7%29%5E2%29------This form of equation allows to easily find vertex, and distance from either focus or directrix.



Parabola has vertex as a minimum point.
Vertex (-7,-3)
-
4p=12
p=3
-
Focus (-7,0)
Directrix y=-6, y=-6

graph%28300%2C300%2C-16%2C4%2C-10%2C10%2C%281%2F12%29x%5E2%2B%287%2F6%29x%2B13%2F12%29