How do you write the quadratic function in standard form given points (-3,-4), (-1,0), (9, -10)?

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Answer 1 · 2017-03-24T09:53:28

#4y = -x^2 +4 x +5#

#ax^2 + bx + c = y#

#3^2 a - 3b + c = -4 Rightarrow c(a, b) = 3b - 9a - 4#

#a - b + c = 0#

#9^2 a + 9b + c = -10#

From the second, #a - b + 3b - 9a - 4 = 0#

#2b - 8a = 4 Rightarrow b(a) = 4a + 2#

#c = 3(4a + 2) - 9a - 4#

#c(a) = 3a +2#

From the third, #81a + 9(4a + 2) + 3a + 2 = -10#

#(81 + 36 + 3)a = -10 - 18 - 2#

#a = - 1/4, b(a) = 2 -1 = 1, c(a) = 2-3/4 = 5/4#

#y = -1/4 x^2 +x +5/4#