Introduction to Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that is defined as the set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the standard form of a parabola's equation?

Back

The standard form of a parabola's equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in the parabola's equation indicate?

Back

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

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 upwards or downwards.

Front

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

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a) from the standard form of the equation y = ax^2 + bx + c.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, which, along with the directrix, defines the parabola.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a fixed line that is perpendicular to the axis of symmetry and is used in conjunction with the focus to define the parabola.

Front

What is the difference between a maximum and minimum in the context of parabolas?

Back

A maximum occurs at the vertex of a downward-opening parabola, while a minimum occurs at the vertex of an upward-opening parabola.

Front

How can you determine if a parabola has a maximum or minimum?

Back

You can determine if a parabola has a maximum or minimum by looking at the sign of the coefficient 'a': if 'a' is negative, it has a maximum; if 'a' is positive, it has a minimum.

Front

What is the significance of the vertex form of a parabola's equation?

Back

The vertex form of a parabola's equation is y = a(x-h)^2 + k, where (h, k) is the vertex. This form makes it easy to identify the vertex and the direction of opening.