Parabola Study Notes (Grade 10, CAPS, South Africa)
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Questions and Answers

What is the equation of the axis of symmetry of the parabola $y = 2x^2 - 4x + 3$?

  • x = -1
  • x = 1
  • x = 1/2
  • x = 2 (correct)
  • If a parabola has a vertex at (2, 3) and passes through the point (4, 7), what is the equation of the parabola?

  • y = (x - 2)^2 + 1
  • y = (x - 4)^2 + 7
  • y = (x - 2)^2 + 2
  • y = (x - 2)^2 + 3 (correct)
  • What is the x-coordinate of the vertex of the parabola $y = x^2 - 6x + 8$?

  • 5
  • 2
  • 3 (correct)
  • 4
  • If a parabola has a focus at (3, 0) and a directrix at x = -1, what is the equation of the parabola?

    <p>y = (x + 1)^2</p> Signup and view all the answers

    What is the equation of the parabola that passes through the points (0, 1), (2, 3), and (4, 7)?

    <p>y = x^2 + 2x + 1</p> Signup and view all the answers

    Study Notes

    Parabola Study Notes (Grade 10, CAPS, South Africa)

    What is a Parabola?

    • A parabola is a type of quadratic curve in the shape of a U, which opens upwards or downwards.

    Equation of a Parabola

    • The standard form of a parabola's equation is y = ax^2 + bx + c, where a, b, and c are constants.
    • The graph of a parabola can be identified by the coefficient of the x^2 term, which is 'a'.

    Characteristics of a Parabola

    • The vertex of a parabola is the turning point, where the curve changes direction.
    • The axis of symmetry is the vertical line that passes through the vertex, and it divides the parabola into two identical halves.
    • The y-intercept of a parabola is the point at which the curve crosses the y-axis.

    Graphing a Parabola

    • To graph a parabola, start by plotting the y-intercept, then use the coefficient 'a' to determine the shape of the curve.
    • If 'a' is positive, the parabola opens upwards. If 'a' is negative, the parabola opens downwards.

    Solving Problems Involving Parabolas

    • To solve problems involving parabolas, use the equation to find the vertex, axis of symmetry, and y-intercept.
    • Use the graph to identify the maximum or minimum value of the parabola, and the x-intercepts.

    Tips for Exam Questions

    • Read the question carefully to identify the type of parabola problem being asked.
    • Use the standard form of the equation to solve the problem.
    • Label the vertex, axis of symmetry, and y-intercept on the graph to ensure accuracy.

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    Description

    Learn about parabolas, including the equation and characteristics of these quadratic curves, specifically for Grade 10 students in South Africa following the CAPS curriculum.

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