# What is the end behavior of g(x)=x^2+4x+4?

May 7, 2018

Both ends go up. Or, as x goes toward positive infinity, y values increase, and as x goes toward negative infinity, y values increase.

#### Explanation:

This is a quadratic function. Think about the parent function for $y = {x}^{2}$. It's a parabola that starts at the origin and goes up on both sides, right?

The degree of a function determines whether its ends go up or down. The degree is the highest exponent on the variable in a polynomial.
This is a second degree polynomial (aka a quadratic) since ${x}^{2}$ is the term with the highest exponent.
In polynomials with even degrees like 2,4,..., the right and left end behavior is the same. If the highest exponent is an even number, this is the case. If that term is positive, both ends go up, like in $y = {x}^{2}$. If that term is negative, both ends go down, like in $y = - {x}^{2}$.