4 2 Parabolas rn a e l l

4. 2 Parabolas rn a e l l l ’ u hat yo W Explain what the focus and directrix of a parabola are. Fill in and label a graphic organizer describing different types of parabolas.

What is a conic? conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse. The conic sections have been studied for thousands of years and have provided a rich source of interesting and beautiful results in Euclidean geometry.

Take a note A parabola is defined as a set of points equidistant from a line (called the directrix) and a point (called the focus). The focus will always lie on the axis of symmetry, and the directrix will always be perpendicular to the axis of symmetry. This definition can be used to derive the equation for a horizontal parabola opening to the right with its vertex at the origin using the distance formula. http: //www. coolmath. com/algebra/25 -conic-sections/03 -introduction-parabolas-01

Deriving the Standard-Form Equation of a Parabola page 175

Explain 1 Writing the Equation of a Parabola with Vertex at (0, 0)

Example 1: Find the equation of the parabola from the description of the focus and directrix. Then make a sketch showing the parabola, the focus, and the directrix.

Answers

Explain 2: Writing the Equation of a Parabola with Vertex at (h, k) p is found halfway from the directrix to the focus:

Answer

Explain 3: Rewriting the Equation of a Parabola to Graph the Parabola A second-degree equation in two variables is an equation constructed by adding terms in two variables with powers no higher than 2. The general form looks like this:

You must combine terms and complete the squares and remember

Explain 4: Solving a Real-World Problem

CW/HW Pages 184 -187