Please enable JavaScript.
Coggle requires JavaScript to display documents.
PARABOLA Learning objectives: 1) Analyze parabolas with the vertex at the…
PARABOLA Learning objectives: 1) Analyze parabolas with the vertex at the origin (0,0) 2) Analyze parabolas with vertex at (h,k) 3) Solve applied problems involving parabolas
1. DEFINITION: A parabola is the collection of all points P in the plane that are the same distance d from a fixed point F as they are from a fixed line D. the point F is called the focus of the parabola, and the line D is its directrix. d(F,P) = d(P,D)
-
the line through focus F and perpendicular to directrix D is called axis of symmetry of the parabola. the point intersection between the parabola with its axis of symmetry is called vertex V. the vertex is midway between the focus and the directrix.
- Parabolas with the vertex at the Origin
-
- Equation of parabola: vertex at (0,0), Focus at (a,0), and directrix x = -a, a>0
-
3. Example 1: Finding the Equation of a Parabola and Graphing it Find an equation of the parabola with vertex at (0,0) and focus at (3,0), graph the equation
-
-
5. PROBLEMS
- analyze (find a, vertex, focus, directix, locus rectum) and graph the equation
- find the equation of the parabola with focus at (0,4) and directrix the line y = -4. Graph the equation
3. Parabolas with vertex at (h,k)
-
3.2 Example 2: Find an equation of the parabola with vertex at (-2,3) and focus at ( 0,3). Graph the equation
-
3.3 Example 3: analyze (find a, vertex, focus, directix, locus rectum) and graph the equation
-
-
-
-