What are the coordinates of the focus of the parabola?
y=1/4x^2−3x+18
The focus of a parabola with equation y = ax^2 + bx + c is given by the coordinates (h, k + 1/4(a/h)^2), where h = -b/2a and k = c - (b^2 - 1)/(4a).
In this case, the equation of the parabola is y = 1/4x^2 - 3x + 18, so a = 1/4, b = -3, and c = 18.
Calculate h:
h = -(-3) / (2 * 1/4) = 6
Calculate k:
k = 18 - ((-3)^2 - 1)/(4 * 1/4) = 18 - (9 - 1) = 10
Calculate the coordinates of the focus:
(6, 10 + 1/4(1/6)^2) = (6, 10 + 1/4(1/36)) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144) = (6, 10 + 1/144)