x^2-2x=8y+23

Question

Write its equation in standard form
Sketch the graph
For Parabolas, identify the vertex, focus, directrix, and axis of symmetry. For Circles, Identify the center and radius. For Ellipses, identify, the center, vertices, co-vertices, and foci. For Hyperbolas, identify the center, vertices, co-vertices, foci, and asymptotes

Answer 1

x^2 -2x = 8y + 23

y= (1/8)(x^2 -2x +1) - 23/8 - 1/8

y= (1/8)(x-1)^2 -24/8

y= (1/8)(x-1)^2 - 3

or

y =[(x-1)^2]/8 -3

vertex = (1, -3) = minimum point

axis of symmetry is x=1

focus = (1, -1)

directrix is y=- 5