Question

3. What is the focus of the parabola?

y = 14x^2 − x − 1

Enter your answer in the boxes.

(______,_______)

Answer 1

@SmokeyBrown

Answer 2

For this one, the focus would occur when x is equal to 1/28, I think.
I used a derivative to find a formula for the slope of the parabola, then solved for x that would make the slope 0.
If I'm not wrong, you should be able to find the y-coordinate by plugging in the x value to the original equation

Answer 3

@Kayden

Answer 4

This is a vertical parabola which opens upwards
we have the general formula
(x - h)^2 = 4p(y - k)   where p is the  y coordinate of the focus

y/14 = x^2 - x /14 - 1/14

add 1/14 to both sides

y/14 + 1 /14 = x^2 - x /14

now complete the square  

y/14 + 1/14 = x^2 - x/14  + 1/28^2

y/14 + 1/14 = (x - 1/28)^2

(x - 1/28)^2 = 1/14( y + 1)


comparing this with the general form:-
4p = 1/14
p =  1/56

so the focus is at (h,p) = (1/28, 1/56)

Answer 5

isn't it (1/28, 139/56) ?