\

The equation is $\"\"$ .

\

Since the $\"\"$ -term is squared, the parabola is vertical.

\

Standard form of the vertical parabola is $\"\"$ .

\

Where

\

Vertex : $\"\"$ ,

\

Focus : $\"\"$ ,

\

Axis of symmetry : $\"\"$ ,

\

Directrix : $\"\"$ .

\

\

The parabola equation $\"\"$ .

\

Write the equation in standard form.

\

$\"\"$

\

To change the expression $\"\"$ into a perfect square trinomial, add $\"\"$ to each side of the equation.

\

Here $\"\"$ coefficient $\"\"$ .

\

So, $\"\"$ .

\

Add $\"\"$ to each side of $\"\"$ .

\

$\"\"$

\

Compare the above eqation with $\"\"$ .

\

Since $\"\"$ , the parabola opens up.

\

Vertex : $\"\"$ ,

\

Focus : $\"\"$ ,

\

Axis of symmetry : $\"\"$ ,

\

Directrix : $\"\"$ .

\

\

Construct a table values to graph the general shape of the curve.

\

The equation is $\"\"$ .

\

Solve for $\"\"$ .

\

$\"\"$

\

$\"\"$

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\"\"

\

$\"\"$

\

\"\"

\"\"

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

\"\"

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

\

Graph :

\

Graph the vertex, focus, axis of symmetry and directrix of the parabola.

\

Plot the points obtained in the above table.

\

Connect those points with a smooth curve.

\

Graph of $\"\"$ :

\

$\"\"$ .

\

$\"\"$

\

\

Vertex : $\"\"$ .

\

Focus : $\"\"$ .

\

Axis of symmetry : $\"\"$ .

\

Directrix : $\"\"$ .

\

Graph of $\"\"$ :

\

$\"\"$ .