Question

What is the focus of the parabola?

y=−14x2−2x−2

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Answer 1

If this is for k12 I took the test and the right answer was (-4, 1)

Explanation:

Answer 2

Explanation:

Given is a parabola

`y=-14x^2-2x-2`

Let us rewrite this in vertex form

`y=-14(x+(1)/(14))^2-(27)/(14)`

Hence vertex =
`((-1)/(14) ,(-27)/(14) )`

Axis of symmetry is

`x=-(1)/(14)`

a=
`(1)/((14)4) =(1)/(56)`

Hence focus would lie on the line of symmetry at a distance of a from vertex

So focus =
`(-(1)/(14) ,-(27)/(14) -(1)/(56) )\\=(-(1)/(14) , -(109)/(56) )`