identify the curve and sketch

Question

identify the Curve represented by the equation: 4x^2 -16x + 12y -8 = 0

Sketch and label its properties.

Answer 1

4x^2-16x+12y-8=0

 

4x^2-16x+16-16+12y-8=0

 

(2x-4)^2+12y-24=0

 

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

 

It is a parabola with vertex at (2,2)

Its axis is x=2

The parabola is inverted Downwards.