# 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?

Aug 1, 2018

"x intercepts" are $\left(- 2 , 0\right) \mathmr{and} \left(2 , 0\right)$ , "y intercept" is $y = - 4$ . End behavior : Up ( As $x \to - \infty , y \to \infty$),
Up ( As $x \to \infty , y \to \infty$),

#### Explanation:

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

leading coefficient is $\left(+\right)$.

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

${x}^{2} - 4 = 0 \mathmr{and} \left(x + 2\right) \left(x - 2\right) = 0 \therefore x = - 2 \mathmr{and} x = 2$ are

two x intercepts at $\left(- 2 , 0\right) \mathmr{and} \left(2 , 0\right)$.

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

$y = 0 - 4 \mathmr{and} y = - 4 \mathmr{and} \left(0 , - 4\right)$ 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 $x \to - \infty , y \to \infty$),

Up ( As $x \to \infty , y \to \infty$),

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