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Find the equation of the parabola that passes through (4,-7) and has vertex (1,-6)

 Oct 2, 2020
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Find the equation of the parabola that passes through (4,-7) and has vertex (1,-6)

 

Hello Guest!

 

\(P_{v}(1,-6)\\ P_1 (4,-7) \)

Because of the symmetry

\(P_2(-2,-7)\)

 

\(\large y=ax^2+bx+c \)

 

\(c=-6\ (vertex)\)

 

  \(-6=\ a\ +\ b\ -\ 6\)      | \(\times 4\)

\(-24=4a+4b-24\)     | subtr.

  \(\underline{-7=16a+4b-6}\)

   \(17=12a+18\\ \ a\ =\frac{17-18}{12}\)

     \(a=-\frac{1}{12}\)

 

  \(-6=-\frac{1}{12}+b-6\)

      \(b=\frac{1}{12}\)

 

  \(The\ equation\ of\ the\ parabola\ is\)  \(y=-\frac{1}{12}x^2+\frac{1}{12}x-6\)

laugh  !

 Oct 2, 2020
edited by asinus  Oct 2, 2020
edited by asinus  Oct 3, 2020

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