Question

How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given `y=x^2-4`?

Answer 1

"x intercepts" are `(-2,0) and (2,0)` , "y intercept" is `y=-4` . End behavior : Up ( As `x -> -oo , y-> oo`),
Up ( As `x -> oo , y-> oo`),

Explanation:

`y=x^2-4`. This is equation of parabola opening up since

leading coefficient is `(+)`.

x intercepts : Putting `y=0` in the equation we get,

`x^2-4=0 or (x+2)(x-2)=0 :. x= -2 and x=2` are

two x intercepts at `(-2,0) and (2,0)`.

y intercept: Putting `x=0` in the equation we get,

`y= 0-4 or y= -4 or (0,-4)` is y intercept.

The end behavior of a graph describes far left

and far right portions. Using degree of polynomial and leading

coefficient we can determine the end behaviors. Here degree of

polynomial is `2` (even) and leading coefficient is `+`.

For even degree and positive leading coefficient the graph goes

up as we go left in `2` nd quadrant and goes up as we go

right in `1` st quadrant.

End behavior : Up ( As `x -> -oo , y-> oo`),

Up ( As `x -> oo , y-> oo`),

graph{x^2-4 [-10, 10, -5, 5]} [Ans]