Key Features of a Parabola

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that can open upwards or downwards, defined by a quadratic function of the form f(x) = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens downwards or upwards.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) for a quadratic function in the form f(x) = ax² + bx + c.

Front

What is the significance of the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, indicating the values of x for which f(x) = 0.

Front

What does the coefficient 'a' in the quadratic function indicate about the parabola?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula for finding the y-coordinate of the vertex of a parabola?

Back

The y-coordinate of the vertex can be found by substituting the x-coordinate of the vertex back into the quadratic function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex.

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the relationship between the axis of symmetry and the vertex?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.