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((-b)/(2a),(-\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((-b)/(2a),(-\Delta+1)/(4a)\right)=\left((-(-3))/(2\cdot14),(-(-999)+1)/(4\cdot14)\right)=\left((3)/(28),(1000)/(56)\right)\\\\\\ \boxed{F=\left((3)/(28),(125)/(7)\right)=\left((3)/(28),17(6)/(7)\right)\approx(0.1,17.86)}`

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

Answer 2

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!