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 (1,0). What is (a, b, c)?
+23245 The graphing formula for a parabola is: y - k = a(x - h)2 where (h, k) = (3, 2)
---> y - 2 = a(x - 3)2
Since (1, 0) is on the parabola ---> 0 - 2 = a(1 - 3)2
-2 = a(-2)2
-2 = a(4)
-½ = a
---> y - 2 = -½(x - 3)2
---> -2(y - 2) = (x - 3)2
---> -2y + 4 = x2 - 6x + 9
---> -2y = x2 - 6x + 5
---> y = -½x2 + 3x - 5/2
