Parabola (Equations, lines and points)

Front

What is a parabola?

Back

A parabola is a 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

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It is the point where the parabola changes direction.

Front

How do you find the vertex of a parabola given in standard form?

Back

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What are x-intercepts of a parabola?

Back

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which helps define its shape. It is located along the axis of symmetry.

Front

What is the directrix of a parabola?

Back

The directrix 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

How do you write the equation of a parabola given its vertex and focus?

Back

Front

What is the significance of the value 'a' in the parabola's equation?

Back

The value 'a' determines the direction and width of the parabola. If 'a' is positive, it opens upwards; if negative, it opens downwards.