find the equation of a parabola with axis parallel to x-axis and passing through (5,4), (11,-2), (21,-4).
$y^2 + Dx + Ey + F = 0$
At (5, 4) $16 + 5D + 4E + F = 0$
$5D + 4E + F = -16$ → equation (1)
At (11,-2) $4 + 11D - 2E + F = 0$
$11D - 2E + F = -4$ → equation (2)
At (21,-4) $16 + 21x - 4E + F = 0$
$21x - 4E + F = -16$ → equation (2)
From equations (1), (2), and (3), D = -2, E = -4, and F = 10 $y^2 - 2x - 4y + 10 = 0$ answer
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$y^2 + Dx + Ey + F = 0$
At (5, 4)
$16 + 5D + 4E + F = 0$
$5D + 4E + F = -16$ → equation (1)
At (11,-2)
$4 + 11D - 2E + F = 0$
$11D - 2E + F = -4$ → equation (2)
At (21,-4)
$16 + 21x - 4E + F = 0$
$21x - 4E + F = -16$ → equation (2)
From equations (1), (2), and (3), D = -2, E = -4, and F = 10
$y^2 - 2x - 4y + 10 = 0$ answer
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