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9.2 Parabolas (Day 1) State whether the graph of the equation is a parabola. 1. y = 2x 2 + 3 2. y + x2 = 7 3. y = 3x + 9 4. y = 6x2 – x + 3 5. y2 = 5 Standard equation of a parabola with vertex at (0, 0) Equation Focus Directrix x2 = 4py y2 = 4px (0, p) (p 0) y = -p x = -p Axis of Symmetry x=0 y=0 Opens Vertically Horizontally NOTE: The directrix is ALWAYS perpendicular to the axis of symmetry‼! Identify the focus and the directrix of the parabola: 𝟑 1. 𝒙 = 𝒚𝟐 2. Y = ½ x2 𝟒 Graph the equation. Identify the focus and directrix. 1. y 2 =- 3x 2. x 2 = 4y Write the standard form of the equation of the parabola with the given focus and vertex at (0. 0). 1. F (0, 3) 2. F (-1, 0) Write the standard form of the equation of the parabola with the given directrix and vertex at (0, 0). 3. y = 2 4. x = -3 A microphone has a parabolic reflector around it to capture sound. The microphone is placed at the focus of the parabola to reflect as much sound as possible. a. Write an equation for the cross section of the reflector. (Scale of 2) (10, 5) b. How high is the microphone above the vertex? 9.2 Parabolas (Day 2) General Form of a Parabola: Form of Equation (y - k) 2 = 4p (x – h) (x – h) 2 = 4p (y – k) ( x + 3)2 = 8(y – 4) Vertex Axis of Symmetry Focus Directrix Direction of Opening 1. Graph (x – 1) 2 = 2(y – 3). Find the Vertex Focus Directrix 2. Graph 4y2 + 4y – 4x – 16 = 0 Find the Vertex Focus Directrix Find an equation for the parabola satisfying the given conditions. 3. Focus (-2, -1); directrix y = 3 4. Focus (4, 1); vertex (7, 1) 5. Vertex (1, -3); directrix x = 5