What is the equation of the parabola that has a vertex at # (-2, 2) # and passes through point # (3,37) #?

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Answer 1 · 2017-03-20T10:22:30

#5y = 7x^2 + 28x + 38#

#y = ax^2 + bx + c#

#V = (-b/(2a), - Delta / (4a)) = (-2, 2)#

#b = 4a#

#Delta = -8a = (4a)^2 - 4ac Rightarrow a ne 0, c = frac{16a + 8}{4} = 4a + 2#

#37 = 9a + 3b + c#

#37 = 9a + 12a + 4a + 2#

#35 = 25a Rightarrow a = 7/5, b = 28/5, c = 38/5#