Question

Which of the equations below could be the equation of this parabola

Answer 1

Answer with explanation:

Vertex of the parabola =(0,0)

Parabola is opening Downwards, in negative direction of y axis.

Equation of the parabola can be written as

x²= -4 a y

Where, (0,-a) is the focus of the parabola.

Line, x=0 is line of symmetry of the parabola,which divides the parabola in two equal halves.

Parabola passes through points (-2,-16) and (2, -16).

(-2)²= -4 a *(-16)

`4= 64a\\\\a=(1)/(16)`

So, focus of the parabola is
`(0,-(1)/(16))`.

Required equation of the parabola is

`x^(2) =-4 * (1)/(16)y\\\\4x^(2) =-y`

Answer 2

Explanation:

Given is a graph of a parabola.

We have to find the equation of the paabola.

We observe from the graph the following points.

i) Vertex is (0,0)

ii) Open downward

iii) Axis of symmetry is y axis or x=0

iv) It passes through (1,4)

The parabola will be of the form

`x^2 =-4ay`

Substitute x=1 and y =4, to find a

1 = -4a(4)

a =
`(-1)/(16)`

Hence equation would be

`x^2 =-(1)/(4) y`