Question

The graph of y+x^2 =0 lies in which quadrants?

Answer 1

The graph of `y+x^2=0` lies in `Q3` and `Q4`.

Explanation:

`y+x^2=0` means that `y=-x^2` and as whether `x` is positive or negative, `x^2` is always positive and hence `y` is negative.

Hence the graph of `y+x^2=0` lies in `Q3` and `Q4`.

graph{y+x^2=0 [-9.71, 10.29, -6.76, 3.24]}

Answer 2

Quadrants 3 and 4.

Explanation:

To solve this equation, the first step would be to simplify the equation `y+x^2=0` by isolating `y` as follows:

`y+x^2 = 0`

`y+x^2-x^2 = 0-x^2`

To isolate `y`, we subtracted `x^2` from both sides of the equation.

This means that `y` can never be a positive number, only `0` or a negative number, since we stated that `y` equals a negative value; `-x^2`.

Now to graph it out:
graph{y=-x^2 [-19.92, 20.08, -16.8, 3.2]}
We can test that the graph is correct simply by using a value for `x`:

`x=2`

`y=-(2^2)`

`y=-4`

If you zoom in on the graph, you can see that when `x=2`, `y=-4`.

Because the graph is symmetrical, when `y=-4`, `x=2 or x=-2`.

And to answer your question, we can see that when we plot the equation out on the graph, the line falls in quadrants 3 and 4.