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The vertex of the parabola below is at the point 3 25 and the point 4 55 is on the parabola What is the equation of the parabola?
Wiki User
∙ 14y ago
Let the polynomial be y = ax^2 + bx + c
The derivative or slope at the minimum is zero: 2ax + b = 0
We have 55 = a (4^2) + b (4) + c
25 = a (3^2) + b (3) + c
and 2a(3) + b = 0 or b = -6a
55 = 16a - 24a + c = -6a + c
25 = 9a -18a +c = - 9a + c
30 = 3a
a = 10
b = -60
c = 55 + 6a = 115
The parabola is y = 10x^2 - 60x + 115
Check using, for instance
http://www.wolframalpha.com/input/?i=evaluate+y+%3D+10x^2+-+60x+%2B+115+at+x%3D3
and
http://www.wolframalpha.com/input/?i=minimize++10x^2+-+60x+%2B+115
Wiki User
∙ 14y ago
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