10.1 Parabolas.

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Presentation transcript:

10.1 Parabolas

Parabola – the graph of a quadratic equation Parabola – the graph of a quadratic equation. The set of all points in a plane that are the same distance from a fixed point called the focus and a fixed line called the directrix. Axis of Symmetry – a line through the focus and perpendicular to the directrix

a > 0 up a < 0 down (0, c) focus (0, -c) y = -c directrix y = c y = ax2 a > 0 up a < 0 down (0, c) focus (0, -c) y = -c directrix y = c x = ay2 a > 0 right a < 0 left (c, 0) focus (-c, 0) x = -c directrix x = c C (the book calls it p) is the distance from vertex to focus or vertex to directrix:

Write the equation v(0, 0) focus (0, -7)

x = -1/8y2 Find focus and directrix

Write this down on your index card

Write the equation in vertex form and find vertex, focus, directrix. x2 + 4x + 8y – 4 = 0

Latus rectum (lr) – a line through the focus that is perpendicular to the axis of symmetry. Its endpoints lie on the parabola. The length of the latus rectum is called the focal diameter.

Find vertex, axis, focus, directrix, focal diameter and equation Find vertex, axis, focus, directrix, focal diameter and equation. 4x – y2 = 2y + 13

Given F(3, 8), directrix is y = 4. Write the equation.

Given F(3, -1) and v(5, -1); write the equation

pg 751 #2-18 even, 26-44 even