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Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
Conic Sections
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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

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