Find a function whose graph is a parabola with vertex (7,8) and that passes thriugh the point (6,-9). f ( x ) = ?

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Find a function whose graph is a parabola with vertex (7,8) and that passes thriugh the point (6,-9).  f  (  x  )  =  ?

yassou1v · Accepted Answer

Step 1In general, equation of parabola with vertex (h,k) is  y  =  a  (  x  −  h      )    2    +  k  .  .  .  (  1  )given vertex   (  h  ,  k  )  =  (  7  ,  8  )  ⇒  y  =  a  (  x  −  7      )    2    +  8...  (  2  )Since parabola passes through (6,-9) eqn (2)  −  9  =  a  (  6  −  7      )    2    +  8    −  9  −  8  =  a  (  7      )    2      ⇒  a  =  −  17So eqn (1)   y  =  −  17  (  x  −  7      )    2    +  8    ⇒  y  =  −  17  (      x    2    +  49  −  14  x  )  +  8    ⇒  y  =  −  17      x    2    −  833  +  238  x  +  8    ⇒  y  =  −  17      x    2    +  238  x  −  825which is required eqn of parabola.

Find a function whose graph is a parabola with vertex (7,8) and that passes through the point (6,-9). f(x)=?

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