Question

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

y = 1/2 x^2

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 .

Compare the above equation with translated form of a parabola .

Vertex .

.

Focus is : .

Equation of the directrix :

Vertex is , focus is , and directrix is .