Question

How do you solve and graph `x^2-1>=4x`?

Answer 1

`(-oo,2-sqrt5)uu(2+sqrt5,+oo)`

Explanation:

`color(blue)"graphing the parabola"`

`x^2-4x-1>=0larr" rearranging"`

`"with "a=1,b=-4,c=-1`

`"find zeros using the "color(blue)"quadratic formula"`

`x=(4+-sqrt(16+4))/2=2+-sqrt5`

`rArrx~~ -0.24" or "x~~ 4.24`

`"since "a>0" then minimum turning point "uuu`

`"to find the vertex "color(blue)"complete the square"`

`x^2-4x+4-4-1`

`rArr(x-2)^2-5`

`rArrcolor(magenta)"vertex "=(2,-5)`

`"the solution to the inequality are the values of x "`
`"above the x-axis"`
graph{x^2-4x-1 [-10, 10, -5, 5]}

`rArr(-oo,2-sqrt5)uu(2+sqrt5,+oo)`