Find the vertex of this parabola. y=-2x+4x+12

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Find the vertex of this parabola. y=-2x+4x+12

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    0
    2021-09-14T20:49:20+00:00

    Answer:

    Vertex of the parabola is ( 1 , 14 ).

    Step-by-step explanation:

    Given Equation of parabola is y=-2^2+4x+12

    We have to find the vertex of the parabola.

    We first convert the given equation of parabola in standard equation of parabola using completing the square method.

    Standard equation of parabola,

    (x-h)^2=4a(y-k)  

    here, ( h , k ) is coordinates of the vertex of the parabola.

    consider,

    y = -2x² + 4x + 12

    y = -2( x² – 2x – 6 )

    y = -2 ( x² – 2x  + 1² – 1² – 6 )

    y = -2 ( x -1 )² – 7 × ( -2 )

    y – 14 = -2 ( x – 1 )²

    (x-1)^2=\frac{1}{2}(y-14)

    By comparing,

    vertex = ( 1 , 14 )

    Therefore, Vertex of the parabola is ( 1 , 14 ).

    0
    2021-09-14T20:49:55+00:00

    Answer:

    (1,14)

    Step-by-step explanation:

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