Question

How do you find the intercept and vertex of `y = x^2 - 4x - 2`?

Answer 1

`"vertex "=(2,-6)," intercepts "=2+-sqrt6`

Explanation:

`"The equation of a parabola in "color(blue)"vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"to obtain this form "color(blue)"complete the square"`

`y=x^2+2(-2)x+4-4-2`

`y=(x-2)^2-6larrcolor(red)"in vertex form"`

`color(magenta)"vertex "=(2,-6)`

`"to obtain the x-intercepts let y = 0"`

`(x-2)^2-6=0`

`(x-2)^2=6`

`color(blue)"take the square root of both sides"`

`x-2=+-sqrt6larrcolor(blue)"note plus or minus"`

`"add 2 to both sides"`

`x=2+-sqrt6larrcolor(red)"exact values"`