Focus and Directrix

Front

What is the focus of a parabola?

Back

The focus is a point that always lies inside your parabola.

Front

What is the directrix of a parabola?

Back

The directrix is a line that always lies outside your parabola.

Front

What is the mini formula we use to find the FOCUS of a parabola?

Back

The focus can be found using the coordinates (h, k + p) or (h, k - p) depending on the orientation of the parabola.

Front

What is the formula for the axis of symmetry of a parabola?

Back

The formula for the axis of symmetry is x = h.

Front

What is the relationship between the distance from any point on the parabola to the focus and the distance to the directrix?

Back

The distance from any point on the parabola to the focus is the same as the distance from that same point to the directrix.

Front

What does the variable 'p' represent in the context of a parabola?

Back

The variable 'p' represents the distance from the vertex to the focus or the vertex to the directrix.

Front

How do you determine the vertex of a parabola given its focus and directrix?

Back

The vertex is located halfway between the focus and the directrix.

Front

What is the standard form of a parabola that opens upwards?

Back

The standard form is y = a(x - h)² + k.

Front

What is the standard form of a parabola that opens downwards?

Back

The standard form is y = -a(x - h)² + k.

Front

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

Back

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