Parts of a Parabola

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 vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum point at its vertex and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum point at its vertex and the arms of the parabola extend downwards.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, which occur when y=0.

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

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

Back

For a parabola in the form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What are the roots or zeros of a parabola?

Back

The roots or zeros of a parabola are the x-values where the parabola intersects the x-axis.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola that is used to define the curve.

Front

What is the directrix of a parabola?

Back

The directrix is a fixed line used in the definition of a parabola, which is perpendicular to the axis of symmetry.