Algebra 2 2.3 Focus of a Parabola

Front

What is the definition of a parabola?

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side. It can open upwards or downwards.

Front

What are the characteristics of a parabola that opens upwards?

Back

A parabola that opens upwards has a vertex at its lowest point, a focus above the vertex, and a directrix below the vertex.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, where all the points on the parabola are equidistant from the focus and the directrix.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a fixed line used in the definition of the parabola, such that any point on the parabola is equidistant from the focus and the directrix.

Front

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

Back

The vertex of a parabola 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, where (h, k) is the vertex and 'a' determines the width and direction of the parabola.

Front

What does the parameter 'a' represent in the parabola's equation?

Back

The parameter 'a' indicates the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you determine if a parabola opens upwards or downwards from its equation?

Back

If the coefficient of the x² term is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.

Front

What is the relationship between the focus and directrix of a parabola?

Back

The focus is a point inside the parabola, while the directrix is a line outside the parabola. Points on the parabola are equidistant from both.

Front

What is the equation of a parabola with focus (0, 3) and directrix y = -3?

Back

The equation is (x - 0)² = 12(y - 0), which simplifies to x² = 12y.