# Equation of horizontal parabola passing through 3 points

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Joel Narvasa Peralta
Equation of horizontal parabola passing through 3 points

find the equation of a parabola with axis parallel to x-axis and passing through (5,4), (11,-2), (21,-4).

Jhun Vert

$y^2 + Dx + Ey + F = 0$

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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