Question

How do you find the x and y intercepts for `f(x) = (x-3)^2 + 17`?

Answer 1

`"y-intercept "=26" no x-intercepts"`

Explanation:

`"to find the intercepts"`

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

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

`x=0toy=(-3)^2+17=26larrcolor(red)" y-intercept"`

`y=0to(x-3)^2+17=0`

`rArr(x-3)^2=-17`

`AAx inRRcolor(white)(x) (x-3)^2>=0`

`rArr" there are no x-intercepts"`
graph{(x-3)^2+17 [-80, 80, -40, 40]}