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

Dec 1, 2014

The standard form of a quadratic is $A {x}^{2} + B x + C$ 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 $y = a {\left(x - h\right)}^{2} + k$ where $h , k$ is the vertex. If we put $y = - 3 {x}^{2}$ 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 $y = - 3 {x}^{2}$, the green is $y = - {x}^{2}$ for comparative sake, and the blue graph is the parent function, $y = {x}^{2.}$