Question

How do you graph `y= -1/4x^2` by plotting points?

Answer 1

See explanation below.

Explanation:

`y` is a parabola with a critical point at `(0,0)`

Since the coefficient of `x^2` is negative `y` has a single maximum value.

Hence, `(0,0)` is an absolute maximum.
and, `y` has no other intercepts on the `x` or `y` axes.

To assist plotting `y` by points it will be necessary to construct a table of points, bearing in mind that `y` is symetric about the `y` axis.
E.g. `(-4,-4), (-2,-1), (0,0), (2,-1), (-4,-4)`

This can be seen from the graph of `y` below: graph{-1/4x^2 [-11.01, 11.49, -8.865, 2.385]}