Question

What are the `x` and `y`-intercepts of `h(x)=2x^2-x`?

Answer 1

`x_("intercept")=0`
`x_("intercept")=1/2`

Explanation:

Write as `y=2x^2-x+0`

`y_("intercept")="the constant"=0`

`x_("intercept")` is at `y=0` so set:

`y=0=2x^2-x`

`y=0=x(2x-1)`

So `x=0 and 2x-1=0`

`x_("intercept")=0`
`x_("intercept")=1/2`

Answer 2

`"x-intercepts "=0,1/2," y-intercept "=0`

Explanation:

`"to determine the x and y intercepts, that is where the"`
`"graph crosses the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercepts"`

`x=0rArry=0-0=0larrcolor(red)"y-intercept"`

`y=0rArr2x^2-x=0`

`rArrx(2x-1)=0rArrx=0" or "x=1/2larrcolor(red)"x-intercepts"`
graph{2x^2-x [-10, 10, -5, 5]}