Question

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

y = 1/4 (x^2 - 2x + 5)

Answer 1

Step 1 :

The parabola equation is .

Write the equation in a translated form of a parabola .

Where is the vertex of the parabola,

p is the directed distance from vertex to focus,

Focus is , and

Equation of the directrix is .

Step 2 :

The parabola equation is .

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

The x coefficient is , .

Compare the above equation with translated form of a parabola .

Vertex .

.

Focus is : .

Equation of the directrix :

Vertex is , focus is , and directrix is .

Comments

Contd........

Step 3 :

The parabola is .

Vertex is , focus is , and directrix is .

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x
0
2
3

Step 4 :

1. Draw a coordinate plane.

2. Plot the vertex and focus of the parabola.

3. Plot the ordered pairs found in the table.

4. Connect those plotted points with a smooth curve.

The graph of the parabola is :

 

Solution :

Vertex is , focus is , and directrix is .

The graph of the parabola is :