Algebra 2: Section 10-2 Parabolas

Algebra 2: Section 10-2 Parabolas Standard: Students explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.  The focus of a parabola is: the fixed point. By definition, a parabola is the set of all points in a plane that are the same distance from a fixed line and a fixed point.  The directrix of a parabola is: the fixed line. The focus and the directrix are equal distance from the vertex. 1 Consider any parabola with equation y  ax 2 and vertex at the origin. a  4c If a  0 , then If a  0, then  The parabola opens upward * The parabola opens downward  The focus is at (0,c) * The focus is at (0,c)  The directrix is y  c * The directrix y  c

1 Consider any parabola with equation x  ay 2 and vertex at the origin. a  4c If a  0 , then If a  0, then  The parabola opens to the right * The parabola opens to the left  The focus is at (c,0) * The focus is at (c,0)  The directrix is x  c * The directrix x  c

The standard from of the equation of a parabola not centered at the origin is y  a(x  h)2  k or x  a(y  k)2  h Where (h,k) is the vertex of the parabola Quick Check Ex. 1) Write an equation for a graph that is the set of all points in the plane that are equidistant from the point F(2,0) and the line x  2 . Vertex (h, k):the point in the middle of the focus and the directrix What is the value of c?

Ex. 2) Write an equation of a parabola with a vertex at the origin and a focus  1  at  ,0 .  2  What is the value of c?

Ex. 3) Identify the vertex, the focus, and the directrix of the graph of x2  6x  3y 12  0 . Then graph the equation.

Assignment page 568 #1-11 odds and #25-35 odds and #36, 38, 40