Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Please help!! ?

Write the equation of the parabola with vertex (3,-1) and y-intercept 2.

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    y - k = a * (x - h)^2

    y - (-1) = a * (x - 3)^2

    y + 1 = a * (x - 3)^2

    y = 2 when x = 0

    2 + 1 = a * (0 - 3)^2

    3 = a * 9

    1/3 = a

    y + 1 = (1/3) * (x - 3)^2

    y = (1/3) * (x - 3)^2 - 1

    Another possibility:

    x - h = a * (y - k)^2

    x - 3 = a * (y - (-1))^2

    x - 3 = a * (y + 1)^2

    y = 2 when x = 0

    0 - 3 = a * (2 + 1)^2

    -3 = a * 9

    -1/3 = a

    x - 3 = (-1/3) * (y + 1)^2

    x = 3 - (1/3) * (y + 1)^2

    Both are valid.

  • 2 months ago

     The equation of the parabola with vertex (3, -1) and y-intercept 2:

     let's write its equation under the form

     y = a(x - 3)^2 - 1 ==> because the vertex is V(3, -1)

     as the y-intercept is 2

     for x=0 we must have

    2 = a (0 - 3)^2 - 1 ==> 9a = 2 + 1 ==> a = 1/3 

     conclusion:

     the equation of the parabola is

     y = 1/3 (x - 3)^2 - 1

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