precalculus/trigonometry

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Find a formula for the given linear function.



The graph of h intersects the graph of y = x^2 at x = -2 and x = 4

  • precalculus/trigonometry -

    Intersections with y=x^2 at x=-2 and x=4 describes two points:

    (-2, y=(-2)^2) and (4, y=4^2)

    Find the line between those two points.

  • precalculus/trigonometry -

    For x = - 2

    y = ( - 2 ) ^ 2 = 4

    ( x1 = - 2 , y1 = 4 )


    For x = 4

    y = 4 ^ 2 = 16

    ( x2 = 4 , y2 = 16 )


    The line through two distinct points (x1, y1) and (x2, y2) is given by

    y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )


    In your case :

    x1 = - 2

    y1 = 4

    x2 = 4

    y2 = 16


    y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )

    y = 4 + [ ( 16 - 4 ) / ( 4 - ( - 2 ) ] * x - ( - 2 ) ]

    y = 4 + [ 12 / ( 4 + 2 ) ] * ( x + 2 )

    y = 4 + ( 12 / 6 ) * ( x + 2 )

    y = 4 + 2 * ( x + 2 )

    y = 4 + 2 x + 4

    y = 2 x + 8

    Proof :

    For x = - 2

    y = 2 * ( - 2 ) + 8 = - 4 + 8 = 4

    ( x1 = - 2 , y1 = 4 )

    For x = 4

    y = 2 * 4 + 8 = 8 + 8 = 16

    ( x2 = 4 , y2 = 16 )

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