1 / 11

Writing Q uadratic E quations when G iven Vertex and Focus/ Directrix .

Writing Q uadratic E quations when G iven Vertex and Focus/ Directrix. Vanessa Ledford Algebra ll. Definition of Focus:. The parabola focus is a point from which distances are measured in forming a parabola and where these distances converge.

jaegar
Download Presentation

Writing Q uadratic E quations when G iven Vertex and Focus/ Directrix .

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Writing Quadratic Equations when Given Vertex and Focus/ Directrix. Vanessa Ledford Algebra ll

  2. Definition of Focus: • The parabola focus is a point from which distances are measured in forming a parabola and where these distances converge. • After changing the quadratic functions to vertex form, the formula for the Focus is (h, k+¼a) • “a” is the number that is in front of the parenthesis. Vertex: (-1,-4) Axis of symmetry: x = -1 Focus: (h, k+1/4a) (-1,-4+¼( 1 )) -4+ (-0.25) = (-1,- 3.75) f(x) = (x+1)2– 4

  3. Definition of Directrix: • A parabola Directrix is a line from which distances are measured in forming a parabola. • After changing the quadratic function in vertex form the formula for the Directrix is y = k – 1/4a Vertex: (-1,-4) Directrix: y = k – 1/4a y = (-4) – ¼(1) y = -4.25 f(x)= (x+1)2 – 4

  4. Definition of the Axis of Symmetry: • The line perpendicular to the directrix and passing through the focus is called the axis of symmetry.

  5. Steps to use: • 1- Make a graph • 2- Find the Vertex • 3- Convert the quadratic function into Vertex Form • 4- Next plug in the numbers for the focus or directrixwhile using the equation that applies to each of them. Ex: If the focus is given then use (h, k+¼a), or if given the directrixuse y = k – 1/4a. In certain cases if your given both the focus and directrix it doesn’t matter which equation to use. • 5- Find the equation to use for finding the leading coefficient -“a” • 6- Then solve for “a” • 7- Finally write the Vertex Form

  6. Showing a problem using formula for Focus: • Write the equation of the quadratic function with a vertex at (0,1) and focus at (0,4). 2. Vertex = (0,1) 6. 1+ (1/4a) = 4 -1 -1 (1/4a) = 3 (4a/1) * (1/4a) = 3 * (4a/1) 1 = 12a (1/12)= (12a)/12 a = 1/12 1. 3. f(x) = a(x – 0)2 +1 a(x)2 +1 4. (h, k + 1/4a) = (0,4) (0, 1 + 1/4a) = (0,4) 5. 1+ 1/4a = 4 7. f(x) = 1/12(x)2 + 1

  7. Showing a problem using formula for Directrix: • Write the equation of the quadratic function with vertex at (1,8) and directrix at y = 3. 2. Vertex = (1, 8) 6. 3 = 8- (1/4)a -8 -8 -5 = (-1/4a) (-4a/1) *-5 = (-1/4a) * (-4a/1) 1 = 20a 1/20= 20a/20 a= 1/20 1. 3. f(x) = a(x-1)2 + 8 4. y = k – 1/4a y = 3 5. 3= 8- 1/4a 7. f(x) = 1/20 (x -1)2 +8

  8. Example 1: • Write the equation of the quadratic function with a vertex at (3, -5) and focus at (3, -4.25). 6. -5 + 91/4a)= -4.25 +5 +5 (1/4a) = 0.75 (4a/1)* (1/4a) = 0.75 * (4a/1) 1= 3a (1/3) = (3a)/3 a= 1/3 2. Vertex = (3, -5) 1. 3. f(x) = a (x- 3)2-5 4. (h, k + 1/4a) = (3, -4.25) ( 3, -5 + 1/4a) = (3, -4.25) 5. -5 + 1/4a = -4.25 7. f(x) = 1/3 (x-3)2 – 5

  9. Example 2: • Write the equation of the quadratic function with focus at (4, 2) and directrix at y = 10. 8/2 = 4 6. 6 + 1/4a = 2 -6 -6 (1/4a) = -4 4a/1 * (1/4a) = -4 * 4a/1 1 = -16a (-1/16) = -16a/-16 a = -1/16 1. 2. Vertex = (4, 6) 3. f(x) = a (x – 1/4a) = (4,2) 4. (h, k = 1/4a) = (4,2) (4, 6 + 1/4a) = (4,2) 5. 6 + 1/4a = 2 7. f(x) = -1/16(x – 4)2 + 6

  10. Example 3: • Write the equation of the quadratic function with focus at (6, 5) and directrix at y = -2. 6. -2 = 1.5 – 1/4a -1.5 -1.5 -3.5 = -1/4a (-4a/1) * -3.5 = (-1/4a) * (-4a/1) 1 = 14a (1/14) = (14a)/14 a= 1/14 7/-2 = -3.5 1. 2. Vertex = (6, 1.5) 3. f(x) = a (x – 6)2 +1.5 4. y = k – 1/4a y = -2 5. -2= 1.5 – 1/4a 7. f(x) = 1/14(x – 6)2 +1.5

  11. Work Cited • 3.6 Focus and Directrix – Writing Quadratics from Info Part ll • Home Work. 3.6 Focus and Directrix • http://www.purplemath.com/modules/conics.htm

More Related