1. Conic Sections
and Parabolas
Chapter 8.1

2. Chapter 8.1
• The study of conic sections, or simply conics.
• Conics are formed by the intersection of a plane
with a pair of cones.

3. Parabolas
Algebraically speaking
• y = ax2 + bx + c
• Has a U-shape.
• Opens with upward or downward.
• The lowest or highest point on such a parabola is
called the vertex.
• It is symmetric about the its axis called the axis of
symmetry.

4. Parabolas

5. Parabolas

6. Standard Form
• The Standard Form of the equation of a parabola
with vertex at (h, k) is:
• (x - h)2 = 4p (y- k), vertical axis; directrix at y = k - p
• (y - k)2 = 4p(x - h), horizontal axis; directrix at x = h - p
• The focus lies on the axis p units from the vertex.
• Find the standard form of the equation of the
parabola with vertex (2, 1) and focus (2, 4)

7. Standard Form

8. Standard Form
• Find the standard form of the parabola with vertex
at the origin and focus (2, 0)

9. Parabola