When putting a quadratic equation in vertex form, I am having difficulty understanding why $h$ is negative when the location of the parabola goes to the right… why is this?
For example, if I have… $y = -2(x-2)^2+9$
I understand that
- $a$ is -2, which means that it is a down-facing parabola
- $k$ is 9, which means that its vertex is positive and above the x-axis
I do not understand that since $k$ is negative, that means the location of the parabola is on the right side of the graph? Shouldn't it be on the left side, since it is negative? Also, when using a Flash quadratic graph displaying tool, it produces these results:
When I specify $h$ to be positive, it comes out to be negative in the quadratic equation. What's up with this?
Thanks
Best Answer
Look at a simpler problem. You know what the graph of $y=x$ looks like, yes? Now think about the graph of $y=x-7$. If you can understand why that's shifted to the right by $7$, and not to the left, you're well on the way to answering your parabola question.