Question

Find the vertex, focus, and directrix of the parabola, and sketch its graph.

Answer 1

Step 1:

The parabola equation is .

Since the term is squared, the parabola is horizontal.

Standard form of horizontal parabola is ,

where , is vertex , focus at and directrix is .

Convert the equation into standard form by using completing square method.

To change the expression into a perfect square trinomial add (half the coefficient)² to each side of the equation.

Compare with .

Vertex .

.

, so the parabola opens to the right.

Focus

Focus.

Directrix .

Directrix .

Axis of symmetry .

Step 2:

Draw the coordinate plane.

Plot the vertex, focus of parabola.

Draw the axis of symmetry and directrix.

Graph the parabola.

.

Solution:

Vertex : .

Focus.

Directrix .

Graph of :

.