Long description: fig6

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A graph showing several parabolas, all opening to the right, plotted on a Cartesian coordinate system.

Alt text: A graph showing several parabolas, all opening to the right, plotted on a Cartesian coordinate system.

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  • The image displays a Cartesian coordinate system with the horizontal axis labeled as \(x\) and the vertical axis labeled as \(y\).
  • Several parabolas are drawn, all opening towards the positive \(x\)-direction.
  • The equations corresponding to the graphed parabolas are listed near the top of the image: \(y^2 = -4a(x + 1)\), \(y^2 = -4ax\), and \(y^2 = -4a(x - 3)\).
  • The graph illustrates a family of parabolas of the form \(y^2 = k(x - h)\), where the focus appears to be at a position determined by the constant \(a\) in the equations provided.

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