# How do you find the domain and range of y=x^2?

Dec 19, 2016

Domain is all real Numbers
Range is all numbers over 0 - (0,$\infty$)

#### Explanation:

One thing that you have to remember is that when you are finding the domain of a polynomial, it is all real number. it runs from $\left(- \infty , \infty\right)$

For finding the range, in a quadratic formula, you have to find when the finction has it's vertex. That is the place that the max or min happens and then you can find the range from there.

in this situaltion we found that the vertex is at the the origin at (0,0)
therefore the range is (0,oo)

Dec 19, 2016

domain: $\left(- \infty , \infty\right)$
range: $\left(0 , \infty\right)$

#### Explanation:

domain: range of values that can be substituted for $x$ in a function

in this case, $x$ needs to have an existing square to be part of the domain of the function $y = {x}^{2}$

any number can be squared, including positive and negative numbers and $\pi$.

This means that the domain goes from $- \infty$ to $\infty$, which is formatted in brackets as $\left(- \infty , \infty\right)$

range: range of values that $y$ can be in a function

in this case, $y$ can be any positive number, including $0$ and ${\pi}^{2}$.

it is always positive since the squares of negative numbers are also positive, e.g. $- {2}^{2} = 4$

this means that the range goes from $0$ to $\infty$, formatted as $\left(0 , \infty\right)$

and here's what it looks like on a graph:
graph{x^2 [-11, 10.885, -5.475, 5.475]}

the graph stretches endlessly on the $x$-axis (though not easily shown here), and the parabola never goes below $0$ on the $y$-axis.