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Questions and Answers
What is the equation of the axis of symmetry of the parabola $y = 2x^2 - 4x + 3$?
If a parabola has a vertex at (2, 3) and passes through the point (4, 7), what is the equation of the parabola?
What is the x-coordinate of the vertex of the parabola $y = x^2 - 6x + 8$?
If a parabola has a focus at (3, 0) and a directrix at x = -1, what is the equation of the parabola?
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What is the equation of the parabola that passes through the points (0, 1), (2, 3), and (4, 7)?
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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.
