How do you graph the quadratic function y=x^2?

May 30, 2018

See below.

Explanation:

$y = {x}^{2}$ is arguably the simplest standard quadratic function.

We can graph the function by plotting points but it is probably more enlightening to consider a few attributes of $y$ in relation to the general quadratic function: $a {x}^{2} + b x + c$

Here, $a = 1$ and both $b \mathmr{and} c = 0$

The graph of any quadratic function is parabolic

Here, $y = 0$ at $x = 0$

And since $a > 0$ we know that $y$ will have a minimum value on its axis of symmetry where $x = \frac{- b}{2 a} = 0$

Thus, ${y}_{\min} = 0$ at $x = 0$

With these results and possibly a few extra points we can draw the graph of $y$ as below.

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