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# Conic Sections

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### Transcript

• 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