classify the graph of the equation -4y^2+5X+3y+7=0 as a circle, a parabola, an ellipse, or a hyperbola.

Answer 1

since there's y^2 but no x^2, it's a parabola, opening to the right:

5x = 4y^2 - 3y - 7
x = 4/5 y^2 - 3/5 y - 7/5
x = 4/5 (y^2 - 3/4 y) - 7/5
x = 4/5 (y^2 - 3/4 y + (3/8)^2) - 7/5 - 4/5 * (3/8)^2
x = 4/5 (y - 3/8)^2 - 121/80

so the vertex is at (-121/80,3/8)

http://www.wolframalpha.com/input/?i=plot+-4y^2%2B5X%2B3y%2B7+%3D+0