Question

The equation of a parabola is given. y=14x2−3x+18
What are the coordinates of the focus of the parabola?

Answer 1

The coordinates of the focus of the parabola are almost the same as coordinates of the vertex:

$F=\left(\dfrac{-b}{2a},\dfrac{-\Delta+1}{4a}\right)\\\\\\y=14x^2-3x+18 \\\\a=14\qquad\qquad b=-3\qquad\qquad c=18\\\\\\\Delta=b^2-4ac=(-3)^2-4\cdot14\cdot18=9-1008=-999\\\\\\ F=\left(\dfrac{-b}{2a},\dfrac{-\Delta+1}{4a}\right)=\left(\dfrac{-(-3)}{2\cdot14},\dfrac{-(-999)+1}{4\cdot14}\right)=\left(\dfrac{3}{28},\dfrac{1000}{56}\right)\\\\\\ \boxed{F=\left(\dfrac{3}{28},\dfrac{125}{7}\right)=\left(\dfrac{3}{28},17\dfrac{6}{7}\right)\approx(0.1,17.86)}$

I don't know which form of coordinates you want as an answer :)

Answer 2

Answer:

The answer is (6, 10)

Also, you might want to make sure you include the division line in 1/4 because 1/4 and 14 result in very different answers, thus the insane answer that someone else gave you!