+817 Suppose that we have an equation $y=ax^2+bx+c$ whose graph is a parabola with vertex $(3,2)$, vertical axis of symmetry, and contains the point $(2,1)$.
What is $(a, b, c)$?
+129771 If the x coordinate of the vertex is 3.....then we have that -b / (2a) = 3
Which neans that -b = 6a ..so.... b = -6a
We know the y coordinate of the vertex is 2 so this means that
2 = a(3)^2 - 6a (3) + c simplifying
2 = 9a - 18a + c
2 = -9a + c
c = 2 + 9a (1)
And the parabola contains the point (2,1) is on the parabola...so we have
1 = a(2)^2 - 6a(2) + c
1 = 4a - 12a + c
1 = -8a + c
c = 1 + 8a (2)
Equate (1) and (2)
2 + 9a = 1 + 8a
2-1 = 8a - 9a
1 = -a
a = -1
And c = 1 + 8(-1) = -7
And b = -6 (-1) = 6
(a, b, c) = (-1 , 6, -7 )
