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meg_poo Group Title

Suppose a parabola has an axis of symmetry at x = –7, a maximum height of 4, and also passes through the point (–6, 0). Write the equation of the parabola in vertex form.

  • one year ago
  • one year ago

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  1. tcarroll010 Group Title
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    Since you have an axis of symmetry at x = -7 and a maximum height of 4, you have the additional point of (-7,4) for the parabola. From symmetry, you have point (-8,0). If you use y = ax^2 + bx + c, you can set up 3 linear equations in 3 unknowns and solve for a, b, and c.

    • one year ago
  2. meg_poo Group Title
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    so like this would be the vertex equation y=-4x^2-56x-192

    • one year ago
  3. tcarroll010 Group Title
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    You have the point (-6,0) from your problem statement plus the 2 points I gave you for 3 points total. Now that you have 3 points, and since they are not collinear (all on the same line), they uniquely determine a polynomial of degree 2, which is a parabola. If you use the equation I gave you and set up 3 substitutions, you will have 3 equations in the unknowns of a, b, and c. So you just have to solve a linear system. Once you get to that point with these 3 points, it's a piece of cake.

    • one year ago
  4. tcarroll010 Group Title
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    Yes, that would be the form, but first you have to solve for a, b, and c from the method I outlined.

    • one year ago
  5. tcarroll010 Group Title
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    Yes, you've got it now.

    • one year ago
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