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# find an equation in standard form of the line containing given points (1,7) (2,2) (4,-35)

The equation of parabola is y=_________

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Find an equation in standard form of the parabola
containing points (1,7) (2,2) (4,-35).

y = ax^2 + bx + c

(1,7): 7 = a(1)^2 + b(1) + c
(2,2): 2 = a(2)^2 + b(2) + c
(4,-35): –35 = a(4)^2 + b(4) + c

a + b + c = 7
4a + 2b + c = 2
16a + 4b + c = –35

Form Augmented Matrix and perform row operations to get reduced row echelon form.

a, b, c
R1 1, 1, 1, 7
R2 4, 2, 1, 2
R3 16, 4, 1,-35

R3 > 4*R2 - R3
R2 > 4*R1 - R2

R1 1, 1, 1, 7
R2 0, 2, 3, 26
R3 0, 4, 3, 43

R3 > 2*R2 - R3

R1 1, 1, 1, 7
R2 0, 2, 3, 26
R3 0, 0, 3, 9

R2 > R2 - R3
R1 > R1 - R3/3

R1 1, 1, 0, 4
R2 0, 2, 0, 17
R3 0, 0, 3, 9

R1 > 2*R1
R3 > R3/3

R1 2, 2, 0, 8
R2 0, 2, 0, 17
R3 0, 0, 1, 3

R1 > R1 - R2

R1 2, 0, 0, -9
R2 0, 2, 0, 17
R3 0, 0, 1, 3

(a,b,c) = (-9/2, 17/2, 3)

y = (-9/2)x^2 + (17/2)x + 3

Check with GeoGebra (or graphing calc):
http://www.wyzant.com/resources/files/267199/find_equation_of_parabola_from_3_points