Question

How do you find the x and y intercepts for `f(x) = -x^2 + 6x + 8`?

Answer 1

`x_("intercepts")-> -2 and -4`

`y_("intercept") =+8`

Explanation:

Given:`" "f(x)=-x^2+6x+8`

The use of the term `f(x)` is that of giving a label (name) to a particular mathematical construct. The `f` is the name and the `(x)` bit means it is applied to `x`

So `f(a)` would mean: `-a^2+6a+8`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine x-intercepts")`

Observe that `2xx4=8" and that "2+4=6`

so we can write: `y=(x+2)(x+4)`

The x-intercept is at `y=0` so :

Set `y=0=(x+2)(x+4)`

Thus for this condition `x=-2 and x=-4`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine y-intercept")`

When the equation is in form `y=ax^2+bx+c` then

`y_("intercept")=c=+8 color(red)(larr" Shortcut")`

You obtain this value by substituting `0" for "x`