How would you solve -2x^2+16x+24y-224 = 0

Question

For this Parabola i also need to know the Center, Focus, Axis of Symmetry, etc.. but i just need the standard form of this equation.

Answer 1

24y=2x^2-16x+224; divide through by 24: y=x^2/12-2x/3+28/3=1/12(x^2-8x+16)+8=1/12(x-4)^2+8.

This is now in standard form y=a(x-h)^2+k where (h,k) is the vertex equal to (4,8). The focus and directrix line can be found from a=1/12 by calculating 1/4a=3. Axis of symmetry is x=h=4.