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)

$4= 64a\\\\a=\frac{1}{16}$

So, focus of the parabola is $(0,-\frac{1}{16})$.

Required equation of the parabola is

$x^{2} =-4 \times \frac{1}{16}y\\\\4x^{2} =-y$

Answer 2

Answer:

Step-by-step 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 =$\frac{-1}{16}$

Hence equation would be

$x^2 =-\frac{1}{4} y$