Find an equation of the plane that passes through the points (1,2,5),(5,4,8), and (2,4,8). v 1 = [ 1 , 2 , 5 ] − [ 5 , 4 , 8 ] = [ − 4 , − 2 , − 3 ] v 2 = [ 2 , 4 , 8 ] − [ 5 , 4 , 8 ] = [ − 3 , 0 , 0 ] v 1 × v 2 = [ 0 , 9 , − 6 ]thus, a x + b y + c z = d , a = 0 , b = 9 , c = − 6to get d we plug 0 ( 5 ) + 9 ( 4 ) − 6 ( 8 ) = − 12Therefore the equation is 9 y − 6 z = − 12Right?

Question

Find an equation of the plane that passes through the points (1,2,5),(5,4,8), and (2,4,8).      v    1    =  [  1  ,  2  ,  5  ]  −  [  5  ,  4  ,  8  ]  =  [  −  4  ,  −  2  ,  −  3  ]      v    2    =  [  2  ,  4  ,  8  ]  −  [  5  ,  4  ,  8  ]  =  [  −  3  ,  0  ,  0  ]      v    1    ×      v    2    =  [  0  ,  9  ,  −  6  ]thus,  a  x  +  b  y  +  c  z  =  d  ,  a  =  0  ,  b  =  9  ,  c  =  −  6to get d we plug   0  (  5  )  +  9  (  4  )  −  6  (  8  )  =  −  12Therefore the equation is   9  y  −  6  z  =  −  12Right?

Hailee West · Accepted Answer

For the quadratic function  f  (  x  )  =  a      x    2    −  b  x  +  cThe standard form is given as  f  (  x  )  =  a  (  x  −  h      )    2    +  kwhere   (  h  ,  k  )  = vertexGiven  f  (  x  )  =  2      x    2    −  6  x    ⇒  f  (  x  )  =  2  (      x    2    −  3  x  )    f  (  x  )  =  2  (      x    2    −  2  ⋅      3    2    x  )    f  (  x  )  =  2  [  (  x  −      3    2        )    2    −  (      3    2        )    2    ]    f  (  x  )  =  2  (  x  −      3    2        )    2    −  2  ⋅      9    4

Find an equation of the plane that passes through the points (1,2,5),(5,4,8) and (2,4,8)

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