Question

How do you find the x and y intercepts for `f(x)=x^2-9x+14`?

Answer 1

y-intercept: `14`
x-intercepts: `2` and `7`

Explanation:

Note that `y` is equivalent to `f(x)`
So we can think of the given equation as
`color(white)("XXX")y=x^2-9x+14`

The y-intercept is the value of `y` when `x=0`.
Given the form of the equation above, clearly:
`color(white)("XXX")`y-intercept `=14`

The x-intercept(s) is/are the value(s) of `x` for which `y=0`
`color(white)("XXX")x^2-9x+14=0`

`rarrcolor(white)("X")(x-7)(x-2)=0`

That is `x=7` or `x=2`

`color(white)("XXX")`x-intercepts: `=7` and `2`