Grade 10 Functions: Hyperbola (Effect of Parameter 'a' on the graph)

Video Description: In this Grade 10 Mathematics lesson, we explore the hyperbolic function and investigate the exact effect that changing the parameter 'a' has on its parent graph. By comparing the parent graph y = \frac{1}{x} with graphs like y = \frac{2}{x} and y = \frac{4}{x}, we unpack how the value of 'a' stretches the hyperbola branches away from the axes. We also break down what happens when 'a' becomes negative a is less than zero, showing you how the graph reflects across the x-axis from the 1st and 3rd quadrants into the 2nd and 4th quadrants. Whether you are prepping for your exams or just trying to master the table method and plotting asymptotes, this step-by-step tutorial makes functions easy to understand! 📊 TIMESTAMPS 00:00 - Introduction to the Hyperbola & the Parent Graph 00:19 - Comparing y-values using the Table Method when a is more than zero. 03:41 - Graphical Analysis: Understanding Decreasing Values 05:02 - Plotting & Analyzing y = \frac4x 06:45 - Key Conclusion: How the value of 'a' stretches the graph 08:02 - Investigating a Negative Parameter (a is less than zero. 10:01 - Understanding X-Axis Reflections (Quadrants 2 & 4) 12:20 - Grade 9 Transformation Recall: How y-values flip 14:40 - Summary of Asymptotes (x = 0 and y = 0) 15:43 - Next Lesson Preview: The Effect of Parameter 'q' 💡 Key Takeaways from this Lesson: When a is more than zero: As 'a' gets larger, the branches of the hyperbola stretch further away from the x-axis and y-axis. When a is less than 0: The graph undergoes a reflection over the x-axis, moving the branches into the second and fourth quadrants. Asymptotes: For these equations, the vertical asymptote is always at x = 0 and the horizontal asymptote is at y = 0. The graph will approach but never touch these lines! If you found this video helpful, please consider subscribing to the channel to join our math community and master your pure mathematics journey! #Grade10Maths #HyperbolaGraph #MathsFunctions #HighSchoolMaths #PureMathematics #Algebra #MathTutorial