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

Answer:

Option (D)

Step-by-step 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 $(h, k+\frac{1}{4a})$.

Given : Vertex → (3, 1) → (h, k)

            Focus → (3, 5) → $(h,k+\frac{1}{4a})$

Therefore, h = 3, k = 1

And, $k+\frac{1}{4a}=5$

$1+\frac{1}{4a}=5$

$\frac{1}{4a}=5-1$

$\frac{1}{4a}=4$

a = $\frac{1}{16}$

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

f(x) = $\frac{1}{16}(x-3)^2+1$

Option (D). will be the answer.