Question

Does the graph `y=-.1x^2` open up or down?

Answer 1

Down - `y_max = 0` at `x=0`
Domain of `y` is `(-oo, +oo)`

Explanation:

`y=0.1x^2`

Since `y_max = 0` at `x=0` and `y` is defined `forall x in RR`
The graph of `y` "opens" down as can be seen from the graph of `y` below.

graph{-0.1x^2 [-10, 10, -5, 5]}

Answer 2

This graph opens down. See explanation.

Explanation:

The graph of a quadratic function opens down if and only if the coefficient next to `x^2` is negative and it opens up if the coefficient next to `x^2` is positive.

In the given function the coefficient is `a=-0.1`, so it is negative, so the graph opens down.

graph{-0.1x^2 [-10, 10, -5, 5]}