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

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.