Question

What are the `y` and `x` intercept(s) of `y=2x^2-4`?

Answer 1

We can set alternately `x=0` and `y=0` to find the intercepts:

Explanation:

To find the y-intercept set `x=0` into your expression and get:
`y=2*0-4=-4`
Sothe coordinates of the y-intercept will be:
`x=0 and y=-4`

To find the x-intercept(s) set `y=0` to get:
`2x^2-4=0`
Rearranging:
`x^2=4/2`
`x^2=2`
`x=+-sqrt(2)`
We have two intercepts of coordinates:
`x=sqrt(2) and y=0`
`x=-sqrt(2) and y=0`

Graphically we can "see" them:
graph{2x^2-4 [-8.625, 11.375, -6.64, 3.36]}

Answer 2

y-intercept: `y=-4`
x-intercepts: `x=-sqrt(2) and x=sqrt(2)`

Explanation:

The y-intercept is the value of `y` when `x=0`
`color(white)("XXX")y=2x^2-4` with `x=0` becomes
`color(white)("XXX")y=2 * 0^2-4 = -4`

The x-intercepts are the values of `x` when `y=0`
`color(white)("XXX")y=2x^2-4` when `y=0` becomes
`color(white)("XXX")0=2x^2-4`
`color(white)("XXX")2x^2=4`
`color(white)("XXX")x^2=2`
`color(white)("XXX")x=+_sqrt(2)`

Answer 3

`y` intercept `-4`, `x` intercepts `+-sqrt2`

Explanation:

`y=2x^2-4`

The `y` intercept is at `x=0`
Where: `y=-4`

The `x` intercept ia at `y=0`
Where: `2x^2-4=0`

`x^2=4/2`

`x=+-sqrt2`

These can be seen on the graph of `2x^2-4` below
graph{2x^2-4 [-6.1, 6.384, -5.12, 1.126]}