Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that is defined as the set of all points 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 located at the midpoint between the focus and the directrix.

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 focus of a parabola?

Back

The focus is a fixed point located inside the parabola where all the reflected rays converge.

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.

Front

How do you find the standard form of a parabola?

Back

The standard form of a parabola that opens upwards or downwards is given by the equation y = a(x - h)² + k, where (h, k) is the vertex.

Front

What does the parameter 'a' represent in the standard form of a parabola?

Back

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

Front

What is the significance of the y-intercept in a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, which can be found by setting x = 0 in the equation of the parabola.

Front

What are the roots or x-intercepts of a parabola?

Back

The roots or x-intercepts are the points where the parabola intersects the x-axis, found by solving the equation y = 0.

Front

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

Back

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