Question

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

Answer 1

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: `ax^2 + bx+c`

Here, `a=1` and both `b 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=(-b)/(2a) =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]}