Question

What are the x– and y–intercepts of the quadratic equation `y = (x – 3)^2 – 25`?

Answer 1

y-intercept: `(-16)`
x-intercepts: `8` and `(-2)`

Explanation:

The y-intercept is the value of `y` when `x=0`
`color(white)("XXX")y=(x-3)^2-25` with `x=0`
`color(white)("XXX")rarr y=(0-3)^2-25 = 9-25 = -16`

The x-intercept(s) is/are the value(s) of `x` when `y=0`
`color(white)("XXX")y=(x-3)^2-25` with `y=0`
`color(white)("XXX")rarr0=(x-3)^2-25`
`color(white)("XXX")rarr 25 = (x-3)^2`
`color(white)("XXX")rarr (x-3)^2=25`
`color(white)("XXX")rarr x-3 = +-5`
`color(white)("XXX")rarr x=8 or x=-2`