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Answer:
4) y = -3(x+2)^2 +4; y = -3x^2-12x-8; ABC=(-3, -12, -8)
5) y = 0.5(x-1)^2-2; y = 0.5x^2-x-1.5; (h,k) = (1, -2)
6) y = -0.3(x+2)^2-6; y = -0.3x^2-1.2x-7.2; (h,k) = (-2, -6)
Explanation:
Writing a quadratic equation through a set of points is most easily done using the regression function of a graphing calculator or spreadsheet.
4) see the first attachment
y = -3(x+2)^2 +4 . . . vertex form
y = -3x^2 -12x -8 . . . standard form (A, B, C) = (-3, -12, -8)
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5) see the second attachment
y = 0.5(x -1)^2 -2 . . . vertex form; vertex = (1, -2)
y = 0.5x^2 -x -1.5 . . . standard form
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6) see the third attachment
y = -0.3(x +2)^2 -6 . . . vertex form; vertex = (-2, -6)
y = -0.3x^2 -1.2x -7.2 . . . standard form
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Doing this without machine help requires you pick a form of the equation you want, fill in the x- and y-values for three of the given points, then solve the resulting equations for the unknown parameters. Usually, we use the form ...
y = ax^2 +bx +c
which will result in three linear equations for a, b, c. Those can be solved by any of the usual methods.