Learning Outcomes: Determine the equation of the parabola with vertex and focus or . (a) Sketch parabolas, recognize the shape and label the focus, vertex and directrix. Determine the vertex, focus and directrix of a parabola by using completing the square method. (b) Exclude: Applications At the end of the lesson, students should be able to 4.3 Parabola C04 - SM025 Page 1
[Open to the left] [Open to the right] Vertex: Focus: Directrix: Axis of symmetry : Standard Equation: General Equation: Graph reference: https://www.desmos.com/calculator/ieceiwsfha Vertex at origin Vertex: Focus: Directrix: Axis of symmetry : Standard Equation: Graph reference: https://www.desmos.com/calculator/3ndjoivylt The Equation of a Parabola (horizontal axis of symmetry) C04 - SM025 Page 2
Given a parabola with the equation . Determine the vertex, focus, directrix and the axis of parabola for the parabola given above. Hence, sketch its graph. Solution : Vertex: Focus: Directrix: Axis of parabola : Graph: Example 1** C04 - SM025 Page 3
[Open downwards] [Open upwards] Vertex: Focus: Directrix: Axis of symmetry : Standard Equation: General Formula: Graph reference: https://www.desmos.com/calculator/xburz1ed6e Centre at origin Vertex: Focus: Directrix: Axis of symmetry : Standard Equation: Graph reference: https://www.desmos.com/calculator/edujybinud The Equation of a Parabola (vertical axis of symmetry) C04 - SM025 Page 4
Given a parabola with the equation . Determine the vertex, focus, directrix and the axis of parabola for the parabola given above. Hence, sketch its graph. Solution : Vertex: Focus: Directrix: Axis of parabola : Graph: Example 2** C04 - SM025 Page 5
Find the equation of a parabola with its focus at and directrix at the line (a) Solution : Vertex: Parabola equation: Find the equation of a parabola with its axis parallel to , vertex at and passing through the point . (b) Solution : Let be the parabola equation At Parabola equation: Example 3 C04 - SM025 Page 6
Determine the equation of parabola obtained by rotating the parabola : anticlockwise through 90o about its vertex. Solution : Parabola Vertex: Focus: Directrix: Parabola Vertex: The equation of Parabola : Example 4 C04 - SM025 Page 7