Characteristics of 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 are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by setting the function equal to zero and solving for x.

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 standard form of a quadratic function?

Back

Front

What does the coefficient 'a' indicate in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the discriminant in a quadratic equation?

Back

Front

How do you find the maximum or minimum value of a parabola?

Back

Front

What is the end behavior of a parabola?

Back

The end behavior of a parabola describes how the function behaves as x approaches positive or negative infinity. For a parabola that opens upwards, both ends go to infinity; for one that opens downwards, both ends go to negative infinity.

Front

What is the vertex form of a quadratic function?

Back