Grade 10 Functions: Parabola (x & y-intercepts, Turning Point & Range) | CAPS Mathematics

In this lesson, Coach Mashabela breaks down everything you need to know about quadratic functions, focusing specifically on the Grade 10 Parabola. You will learn step-by-step how to algebraically calculate and visually verify key properties of a parabolic graph following the CAPS curriculum. Whether you are preparing for your exams or trying to master functions, this video makes algebra easy to understand. We cover: How to find the x-intercepts (letting y = 0) and handling square roots. How to find the y-intercept (letting x = 0). Understanding the Turning Point and identifying the Minimum Value. Determining the Range of a parabola using interval notation. We unpack three specific equations to show how shifting the graph changes these key points: f(x) = x^2 (The parent graph) g(x) = x^2 - 1 (Vertical shift downward) h(x) = x^2 + 1 (Vertical shift upward – introducing undefined real roots) 📌 Timestamps & Chapters [00:00] - Introduction to Parabola Properties [00:22] - Finding x and y Intercepts for f(x) = x^2 [02:00] - Graphical Proof of the Parent Graph [02:30] - Calculating x-intercepts for g(x) = x^2 - 1 (Plus or Minus rule) [05:00] - Graphical Proof of g(x) = x^2 - 1 [05:34] - Calculating the y-intercept for g(x) = x^2 - 1 [06:47] - Finding Intercepts for h(x) = x^2 + 1 (Why x is Non-Real/Undefined) [09:50] - Introduction to the Turning Point (Increasing vs. Decreasing functions) [11:15] - Understanding the Minimum Value (a is more than 0) [12:08] - Finding the Range for g(x) = x squared- 1 [12:42] - Finding the Range for f(x) = x squared [13:01] - Finding the Turning Point, Minimum Value, and Range for h(x) = x squared+ 1 [14:03] - Preview of Next Lesson: Finding the Equation of a Parabola 💡 Key Takeaways from this Lesson: The x-intercept Rule: Always write down "Let y = 0" for the examiner before solving! Non-Real Roots: When you try to take the square root of a negative number (like \square root-1), the x-intercept is undefined in the high school number system—meaning the graph does not cross the x-axis. Interval Notation: Remember to use a square bracket [ for included minimum values and a round/curly bracket ) for infinity. If you found this math tutorial helpful, please consider subscribing, liking, commenting, and sharing with your classmates! 🔔 Subscribe for more Grade 10 - 12 Mathematics tutorials. Next up: How to determine the equation of a parabolic graph! #Grade10Maths #Parabola #FunctionsAndGraphs #CAPSMathematics #HighSchoolMath #TurningPoint #MathTutorial #CoachMashabela