Question

Select the correct answer

The vertex of a parabola is at the point (3,1), and its focus is at (3,5), What function does the graph represent?

Answer 1

Option (D)

Explanation:

Vertex form of the parabola will be,

f(x) = a(x - h)² + k

Where (h, k) is the vertex and focus will be
`(h, k+(1)/(4a))`.

Given : Vertex → (3, 1) → (h, k)

Focus → (3, 5) →
`(h,k+(1)/(4a))`

Therefore, h = 3, k = 1

And,
`k+(1)/(4a)=5`

`1+(1)/(4a)=5`

`(1)/(4a)=5-1`

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

a =
`(1)/(16)`

By substituting these values in the equation, function representing the parabola will be,

f(x) =
`(1)/(16)(x-3)^2+1`

Option (D). will be the answer.