[Math] Quadratic vertex form – negative $h$ means it’s on the right side of the graph

algebra-precalculusquadratic-formsquadratics

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:

graphing a parabola

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.

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