(a)

The distance between vertex and focus of each parabolas is

(i) The parabola equation is .

The standard form  of parabola is ,

where is distance between vertex and focus, Vertex : and Focus : .

can be written as .

Hence .

The distance between vertex and focus is .

Where and

Focus point of the parabola is

(ii) The parabola equation is .

can be written as .

Hence .

The distance between vertex and focus is .

Where and .

Focus point of the parabola is

(iii) The parabola equation is

can be written as .

Hence .

The distance between vertex and focus is

Where and

Focus point of the parabola is

(b)

Graph:

Graph the parabola , and .

Plot the focal points , and .

(c)

Observe the graph,

As the focus is moved farther away from the vertex, the parabola is wider.

(d)

The parabola can be writen , where and the vertex .

If a parabola is narrow then distance between the focus and vertex is small.

Assume   then the parabola equation having vertex is .

.

(e)

The parabola equations are , and .

Since term is squared, the parabola opens downwards.

The parabola have a vertex of .

The parabola equation is .

Rewrite the equation.

, where and .

Focus point of the parabola is

The parabola equation is .

Rewrite the equation.

, where and .

Focus point of the parabola is .

The parabola equation is

Rewrite the equation.

, where and .

Focus point of the parabola is

Graph :

Graph the parabola , and .

Plot the focal points , and .

(a) (i)The distance between vertex and focus is .

(ii)The distance between vertex and focus is .

(iii)The distance between vertex and focus is .

(b)

Graph of the parabola , and is

(c) As the focus is moved farther away from the vertex, The parabola is wider.

(d) The parabola equation

(e) 

Graph of the parabola , and is