Question

How do I graph the quadratic equation `y=-3x^2`?

Answer 1

The standard form of a quadratic is `Ax^2+Bx+C` where C is the y-intercept.

In this case it looks as though `C=0` giving us some information. Also, the `A` is negative telling us the parabola opens down.

Now, if we look at the vertex form of a quadratic, we get `y=a(x-h)^2+k` where `h,k` is the vertex. If we put `y=-3x^2` into the vertex form, we see that the vertex is at the origin, `0,0`.

Additionally, the `-3` is going to "close" the parabola so that it is closer to the y-axis than is the parent function `y=x^2`.

Finally, the graph will look like the following...

The red graph is the function `y=-3x^2`, the green is `y=-x^2` for comparative sake, and the blue graph is the parent function, `y=x^2.`