Question

How do you determine whether the function `y=x^2` is concave up or concave down and its intervals?

Answer 1

`y=x^2` is concave up with an interval of `(-oo,+oo)`

Explanation:

A polynomial function is concave up (opens upward) if the coefficient of `x^2` is greater than `0`. If the coefficient of `x^2`is greater than `0` then `yrarr+oo` as `xrarr+-oo`

Conversely if the coefficient of `x^2` is less than `0` the parabola opens downward.