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

1 Answer
Alan N.
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: #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]}

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