Pre-Calculus Honors
9.1 Introduction to Conics: Parabolas
Mrs. Iverson
Name ___________________________
Date _____________ Period ________
Warm Up
1) Sketch the following parabola: y  2 x
2
Vertex: ___________
Essential Question: What is a parabola?
Learning Targets: 5.9.1: Write equations of parabolas in standard form.
5.9.2: Identify the vertex, focus, and axis of symmetry of parabolas.
5.9.3: Solve real-life problems using parabolas.
CONICS: the intersection of a plane and a double-napped cone.
Parabola: the set of all points that are equidistant from a fixed line and a fixed point.
(symmetrical curve formed by the intersection of a cone with a plane parallel to its side)
Standard Equation of a Parabola:
The standard form of the equation of a parabola with vertex (h, k) is as follows.
Example 1: Find the following information for each parabola then sketch its graph.
A) y  2 x 2
Vertex:_____________
Focus:______________
Axis of Symmetry: Vertical or Horizontal
1
B) ( x  3)   ( y  2)2
3
Vertex:_____________
Focus:______________
Axis of Symmetry: Vertical or Horizontal
C) y 2  4 y  4 x  0
Vertex:_____________ Focus:______________
Axis of Symmetry: Vertical or Horizontal
D) 4 y 2  4 y  4 x  5  0
Vertex:_____________ Focus:______________
Axis of Symmetry: Vertical or Horizontal
Example 2: Find the standard form of the equation of the parabola with vertex at the origin.
5 
A) Focus:  , 0 
2 
(-2,6)
B)
C) Axis of Symmetry: Vertical
going through (-3,-3)
Example 3: Find the standard form of the equation of the parabola.
A)
(4.5,4)
(5,3)
B) Vertex: ( -2, 1) & Directrix: x=1
9
C) Vertex: (3, -3) & Focus: (3,  )
4
PRACTICE 9.1
1) Find the vertex and focus of each parabola. Then sketch the parabola.
A. x 2  2 x  8 y  9  0
B. x 2  12 y  10 x  37  0
2) Find the standard equation of a parabola with…
A. vertex (0,0) and directrix x  5 / 2 .
3)
C. x 2  4 x  8 y  4  0
B. vertex (1,4) and focus at (1,7)
4)
5)
6)