Parabolas

Front

What is a parabola?

Back

A parabola is a 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

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a) from the quadratic equation in the form y = ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

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

Front

What are the zeros of a parabola?

Back

The zeros of a parabola are the x-values where the graph intersects the x-axis, also known as the roots or solutions of the quadratic equation.

Front

How can you determine the number of zeros a parabola has?

Back

The number of zeros can be determined using the discriminant (D = b^2 - 4ac) from the quadratic formula. If D > 0, there are 2 zeros; D = 0 means 1 zero; D < 0 means no real zeros.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which is used in the definition of a parabola as the point from which distances to the directrix are measured.