How do you graph y=x^2-2x-8y=x22x8?

1 Answer
Jan 2, 2018

Refer explanation.

Explanation:

  • METHOD 1: ALGEBRA

y =x^2-2x-8y=x22x8 is quadratic in xx. a=1,b=-2,c=-8a=1,b=2,c=8

As coefficient of x^2x2 is positive so, its graph will be mouth opening upward parabola.

Check discriminant of the quadratic to examine the nature of the roots.
D=b^2-4acD=b24ac
D=4+32=36D=4+32=36
As D>0D>0, the roots of quadratic will be real and unequal. Also, we can find roots of y=0y=0 that are x=4,-2x=4,2

Here, y=-8y=8 at x=0x=0

The minima of the above quadatic is at x=-b/(2a)=2/2=1x=b2a=22=1
The value of quadratic at minima = -D/(4a) =-36/4= -9=D4a=364=9

By analysing above all points graph will be
graph{x^2-2x-8 [-25.65, 25.65, -12.83, 12.82]}

  • METHOD 2:CALCULUS

Find dy/dxdydx and (d^2y)/dx^2d2ydx2 . Also check the nature of the graph by derivative tests.