Question

What is the equation of the parabola?

Answer 1

Answer:

Option D.

Step-by-step explanation:

The vertex form of a parabola along y-axis is

$y=a(x-h)^2+k$      ...(1)

where, (h,k) is vertex and a is a constant.

From the given graph it is clear that the vertex of the parabola is (0,2). So, h=0 and k=2.

$y=a(x-0)^2+2$

$y=ax^2+2$    ...(2)

The graph passing through (6,5). Substitute x=6 and y=5 in the above equation.

$5=a(6)^2+2$

$5-2=36a$

$3=36a$

$\frac{3}{36}=a$

$\frac{1}{12}=a$

Substitute $a=\frac{1}{12}$ in equation (2).

$y=\frac{1}{12}x^2+2$

Therefore, the correct option is D.