Conic Sections
- 1. Conic Sections Chapter 10: Section 1
- 2. Types of Conic Sections Parabola Circle Ellipse Hyperbola
- 3. Parabola Standard Formulas y = ax 2 + bx + c Or x = ay 2 + by + c
- 4. Circle Standard Formula (x-h) 2 + (y-k) 2 = r 2 where the center of the circle is (h,k) and radius r
- 5. Ellipse Standard Formulas x 2 + y 2 = 1 a 2 b 2 or x 2 + y 2 = 1 b 2 a 2
- 6. Hyperbola Standard Formulas x 2 - y 2 = 1 a 2 b 2 or y 2 - x 2 = 1 a 2 b 2
- 7. X-intercepts The x-intercepts are the point(s) where the line crosses the x-axis
- 8. How do I find the x-intercept? Look at the graph if one is provided. Where ever the line crosses the x-axis, that is an x-intercept. X-intercept = 0
- 9. What are the x-intercepts? x-intercept = +3 and -3 No x-intercepts
- 10. Find the x-intercepts X-intercepts = +3 and -3 X-intercepts = +2 and -2
- 11. How to find the x-intercept if given the equation At all points on the x-axis, the value of y is zero. So, if zero is substituted for y in the equation it will yield the x-intercept(s), IF it exists. y = 2x 2 0 = 2x 2 Substitute 0 for y 0/2 = x 2 Divide both sides by 2 0 = x 2 √ 0 = √x 2 Take the square root of both sides 0 = x x-intercept = 0
- 12. Example #1 y = 3x 2 + 2 0 = 3x 2 + 2 Substitute 0 for y -2 = 3x 2 Subtract 2 from both sides -2/3 = x 2 Divide both sides by 3 √ -2/3 = √x 2 Take the square root of both sides You cannot take the square root of a negative number…so this equation has no x-intercepts .
- 13. Example #2 x 2 + y 2 = 25 x 2 + (0) 2 = 25 Substitute 0 for y x 2 = 25 √ x 2 = √25 Take the square root of both sides x = ±5 x-intercept = +5 and -5
- 14. How do I find the domain? The domain is all the x-values on the graph. x ≥ -6 x ≤ 6 -6 0 6
- 15. Example #1 The domain is all the x-values on the graph. Domain: all real numbers
- 16. Example #2 Domain: x ≥ -3 x ≤ 3
- 17. Example #3 Domain: x ≤ -2 x ≥ 2