key characteristics of parabolas

Front

What is a parabola?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a parabola, depending on its orientation.

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, passing through the vertex.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola intersects the y-axis, represented as (0, y).

Front

What is the x-intercept of a parabola?

Back

The x-intercept(s) are the points where the parabola intersects the x-axis, represented as (x, 0).

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if its vertex is the minimum point, and the arms of the parabola extend upwards.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if its vertex is the maximum point, and the arms of the parabola extend downwards.

Front

What is the domain of a parabola?

Back

The domain of a parabola is all real numbers, as it can extend infinitely in the horizontal direction.

Front

What is the range of a parabola that opens upwards?

Back

The range of a parabola that opens upwards is from the y-coordinate of the vertex to positive infinity.

Front

What is the range of a parabola that opens downwards?

Back

The range of a parabola that opens downwards is from negative infinity to the y-coordinate of the vertex.