1 / 6

Intro to Conics – Parabolas

Intro to Conics – Parabolas. I. Parabolas. A) Quadratic form: y = ax 2 + bx + c or x = ay 2 + by + c. B) Directions parabolas open. 1) y = ax 2 + bx + c 2) x = ay 2 + by + c y = – ax 2 + bx + c x = – ay 2 + by + c. Intro to Conics – Parabolas.

jerryw
Download Presentation

Intro to Conics – Parabolas

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. Intro to Conics – Parabolas I. Parabolas. A) Quadratic form: y = ax2 + bx + c or x = ay2 + by + c. B) Directions parabolas open. 1) y = ax2 + bx + c 2) x = ay2 + by + c y = – ax2 + bx + c x = – ay2 + by + c

  2. Intro to Conics – Parabolas II. Parts of a Parabola. A) Vertex point: the min / max point on a parabola. 1) Formula for finding the vertex of a parabola… a) for y = ax2 + … is ( – b/2a , plug it in) b) for x = ay2 + … is (plug it in , – b/2a) B) Focus point: a special point located inside the parabola. C) Axis of Symmetry: the line of symmetry that divides a parabola into two equal halves. 1) Goes thru the vertex point. (vert: x = # or horiz: y = #) D) Directrix line: a line that is equal distant from the focus to the parabola (at a right angle).

  3. Intro to Conics – Parabolas III. Finding the Focus and Directrix of a Parabola. A) Focus point: (only works for ay = bx2 or ax = by2) 1) Isolate the squared term. 2) Divide the side that doesn’t have the exponent by 4 (or multiply by ¼ whichever is easier). 3) The # in front of the non-squared term is the focus. (the squared letter gets a zero coordinate value). (the non-squared term gets the focus number) Examples: If you have already done the 3 steps above, then … x2 = 5y y2 = – 5/7x Focus = ( 0 , 5 ) Focus = ( – 5/7 , 0 )

  4. Intro to Conics – Parabolas III. Finding the Focus and Directrix of a Parabola. B) The Directrix: you need to find the focus first. 1) The equation for the directrix line is found by … a) Changing the sign of the focus. b) Whichever letter had the focus is the letter that is needed for the directrix equation. Examples: Focus = ( 0 , 5 ) Focus = ( – 5/7 , 0 ) Directrix is y = – 5 Directrix is x = 5/7

  5. Intro to Conics – Parabolas Examples: Find the focus point of the parabola. 1) – 2x2 = y 2) 1/25y2 = x 3) 4y = 6x2 (divide by – 2) (multiply by 25) (divide by 6) x2 = – ½ y y2 = 25x 4/6y = 2/3y = x2 (multiply by ¼) (divide by 4) (multiply by ¼) x2 = – 1/8y y2 = 25/4x 2/12y = 1/6y = x2 Focus (0 , –1/8) Focus (25/4, 0) Focus (0, 1/6) Directrix y = 1/8 Directrix x = -25/4 Directrix y = -1/6

  6. Intro to Conics – Parabolas IV. Sketching Parabolas. A) Find and graph the Vertex point. (– b/2a , plug it in ) or ( plug it in , – b/2a ) B) Determine the direction the parabola opens. 1) y = ax2 + … opens up or down (+ is up, – is down). 2) x = ay2 + … opens left or right (+ is right, – is left). C) Determine the “slope” of the parabola. 1) Taller ( a > 1 ) draw a narrow parabola. 2) Shorter ( 0 > a > 1 ) draw a wide parabola.

More Related