Question

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

Answer 1

y intercept: `color(red)(-2)`
vertex at `color(red)(""(x,y)=(2,-6))`

Explanation:

The y-intercept is the value of `y` when `x=0` (that is for point on the Y-axis)
for the given equation
`color(white)("XXX")y=x^2-4x-2`
replacing `x` with `0` gives
`color(white)("XXX")y=0^2-4**0-2 = -2`

The easiest way to find the vertex is to convert the given equation into "vertex form": `y=m(x-a)^2+b` with vertex at `(a,b)`
`color(white)("XXX")y=x^2-4x-2`

`color(white)("XXX")y=1(x^2-4xcolor(magenta)(+4))-2color(magenta)(-4)`

`color(white)("XXX")y=1(x-2)^2-6`
which is the vertex form with vertex at `(2,-6)`

For verification purposes, here is teh graph of the original equation:
graph{x^2-4x-2 [-4.636, 7.854, -6.12, 0.12]}