Notes Creating Parabola Equations If the directrix is

Notes -Creating Parabola Equations If the directrix is below or above the focus(graph opens up or down) equation is: (y – k) = 1 (x – h)2 if graph opens up (directrix is under focus) 4 p or (y – k) = - 1 (x – h)2 if graph opens down(directrix is above focus) 4 p If the directrix is to the left or right of the focus, (graph opens left or right), then equation is: (x – h) = 1 (y – k)2 if graph opens right (directrix is left of focus) 4 p or (x – h) = - 1 (y – k)2 if graph opens left(directrix is right of focus) 4 p Steps to create equation given vertex and focus: 1. Plot focus and vertex on same graph. 2. Find distance from vertex point to focus on graph, This = p. 3. Start at vertex, go p spaces in the opposite direction from the focus, plot a point here and draw the directrix through this point. 4. Use directrix to determine which way graph opens and write correct version of parabola equation. (see above) 5. Plug in vertex #’s in for h and k in form. 6. Multiply p found by 4 and put under 1 in fraction in form. Examples: 1. Vertex (3, -2) , focus (3, -6) 3. Vertex (-5, 3), focus (-5, 9) 2. Vertex (-4, -1) focus (2, -1) 4. Vertex (-3, -4), focus (1, -4)

Notes -Creating Parabola Equations If the directrix is below or above the focus(graph opens up or down) equation is: (y – k) = 1 (x – h)2 if graph opens up (directrix is under focus) 4 p or (y – k) = - 1 (x – h)2 if graph opens down(directrix is above focus) 4 p If the directrix is to the left or right of the focus, (graph opens left or right), then equation is: (x – h) = 1 (y – k)2 if graph opens right (directrix is left of focus) 4 p or (x – h) = - 1 (y – k)2 if graph opens left(directrix is right of focus) 4 p Steps to create equation given vertex and directrix: 1. Plot vertex and directrix on same graph. 2. Find distance from vertex point to point on directrix directly across from it, this = p. 3. Start at vertex, go p spaces in the opposite direction from the directrix, plot a point here, this is the focus. 4. Use directrix to determine which way graph opens and write correct version of parabola equation. (see above) 5. Plug in vertex #’s in for h and k in form. 6. Multiply p found by 4 and put under 1 in fraction in form. Examples: 1. Vertex (5, 1) , directrix y = -2 2. Vertex (-2, 4) , directrix x = 3 3. Vertex (3, -6) , directrix x = -1 4. Vertex (0, -3) , directrix y = 3

Creating Parabola Equations Practice Find the equation of a parabola given the following information. Also, list the missing information for each problem(directrix or focus) 1. Vertex (0, -4) , directrix x = 3 2. Vertex (-7, 1) , directrix y = -4 3. Vertex (5, -9) , directrix x = 1 4. Vertex (6, 0) , directrix y = -8 5. Vertex (-6, -5) , directrix y = -3 6. Vertex (2, -3) , directrix x = 8 7. Vertex (5, 0) , focus (5, 7) 8. Vertex (-1, 4) focus (4, 4) 9. Vertex (2, -5), focus (-4, -5) 10. Vertex (4, 3), focus (4, -1) 11. Vertex (-3, 2), focus (-1, 2) 12. Vertex (-5, -6), focus (-5, 1)

Ticket out the door Find the equation of a parabola given the following information. Also, list the missing information for each problem(directrix, vertex, or focus) 1. Vertex (-2, 4) , directrix x = 1 2. Vertex (6, 3) , directrix y = -1 3. Vertex (0, -5) , focus ( -2, -5) 4. Vertex (8, 3) focus (8, -4)