1 / 21

7.1. Parabolas

7.1. Parabolas. Mat 151 Chapter 7. 7.1. PARABOLA. Vertical Parabola – x is squared but not y. Vertex (h, k) If a > 0 Opens UP If a < 0 Opens DOWN If a > 1 then parabola is SKINNY ( or a < - 1) If - 1 < a < 1 parabola is FAT. 7.1. PARABOLA. For every parabola find:.

morpheus-zephyr
Download Presentation

7.1. 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. 7.1. Parabolas Mat 151 Chapter 7

  2. 7.1. PARABOLA • Vertical Parabola – x is squared but not y • Vertex (h, k) • If a > 0 Opens UP • If a < 0 Opens DOWN • If a > 1 then parabola is SKINNY ( or a < - 1) • If - 1 < a < 1 parabola is FAT

  3. 7.1. PARABOLA • For every parabola find: • Find the vertex • Find the y and x intercepts • Graph the parabola • Find the axis of symmetry for parabola

  4. 7.1. PARABOLA • Graph parabola find: • Vertex @ (4,0) • X - intercept @ (4,0) • Y - intercept @ (0,16) • Parabola opens up • Axis of symmetry for parabola is vertical line x = 4

  5. 7.1. PARABOLA • Graph parabola find: • Vertex @ (3, - 2) • X - intercept @ (4.41,0) and (1.59,0) • Y - intercept @ (0,7) • Parabola opens up • Axis of symmetry for parabola is vertical line x = 3

  6. 7.1. PARABOLA • Horizontal Parabola – y is squared but not x • Vertex (h, k) • If a > 0 Opens to the right • If a < 0 Opens to the left • If a > 1 then parabola is SKINNY ( or a < - 1) • If - 1 < a < 1 parabola is FAT

  7. 7.1. PARABOLA • Graph parabola find: • Vertex @ (2,0) • X - intercept @ (2,0) • Y - intercept – No y intercept • Parabola opens to the right • Axis of symmetry for parabola is horizontal line y = 0

  8. 7.1. PARABOLA • Graph the horizontal parabola:

  9. 7.1. Application of PARABOLA • If an object is thrown upward with initial velocity of 32 ft/sec, then its height after t seconds is: • Find the maximum height attained by the object. • Find the total time in air. • HINT: • The vertex of parabola h = -16t2 + 32t is information that has the maximum height and also half of total time in air.

  10. 7.1. Application of PARABOLA • The revenue received from selling x stereos is given by the formula: • Find how many stereos must be sold to obtain the maximum revenue? • Find the maximum revenue. • HINT: • The vertex of parabola R = -0.5x2 + 80x - 100 is information that has the maximum height and also half of total time in air.

  11. 7.2 EQUATION OF ELLIPSE An equation of the ellipse with center at (0, 0) and foci at (- c, 0) and (c, 0) is: Because a > b the major axis is the x-axis The vertices are at (-a, 0) and (a, 0).

  12. Minor Axis y P = (x, y) Major Axis x V1 F1 F2 V2 ELLIPSE An ellipse is the collection of points in the plane the sum of whose distances from two fixed points, called the foci, is a constant.

  13. GRAPH OF ELLIPSE y F2=(c, 0) F1=(-c, 0) (0, b) x V2=(a, 0) V1=(-a, 0) (0, -b)

  14. y (h + c, k) (h - c, k) Major axis (h - a, k) (h, k) (h + a, k) x Ellipse with Major Axis Parallel to the x-Axis where a > b and b2 = a2 - c2.

  15. y (h, k + a) (h, k + c) (h, k) (h, k - c) x Major axis (h, k - a) Ellipse with Major Axis Parallel to the y-Axis where a > b and b2 = a2 - c2.

  16. 7.2. ELLIPSE • Graph the ellipse: • Center @ (0,0) • X - intercepts @ (- 3,0) and (3,0) • Y - intercepts @ (0,- 5) and (0,5) • a = 5 • b = 3 (0, 5) (-3, 0) (3, 0) x (0, -5)

  17. 7.2. ELLIPSE • Graph the ellipse: • Center @ (0,0) • a = 4 • b = 3 • X - intercepts @ (- 4,0) and (4,0) • Y - intercepts @ (0,- 3) and (0,3) y (-3, 0) x (0, -4) (0, 4) (3, 0)

  18. y (-2, 2) x (-6, -1) (2, -1) (-2, -1) (-2, -4) 7.2. ELLIPSE • Graph the ellipse: • Center @ (-2 , - 1) • Horizontal axis is a = 4 • Vertical axis is b = 3 From the center: - Go 3 units UP - Go 3 units DOWN - Go 4 units RIGHT - Go 4 units LEFT Connect four points

  19. y b = 15 x (-6, -1) 2a = 20 7.2. Application of ELLIPSE • A one way road passes an overpass in the form of half of an ellipse, 15 ft high at the center and 20 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass? From the graph: 2a = 20 a = 10 ft b = 15 ft h = 0 k = 0

  20. 7.2. Application of ELLIPSE • Solution: The height of truck is x If we have equation for ellipse, and substitute x = - 6 or x = 6, we will find the y that represent the height of truck. (-6,y) (6,y) b = 15 h (-6, -1) 12ft 2a = 20 If we consider ellipse centered @ (0,0) then a = 10 and b = 15 If we substitute x = 6: Height of the truck

  21. V2= (0, a) F2 = (0, c) (-b, 0) (b, 0) x F1= (0, -c) V1= (0, -a) y

More Related