IM2 Characteristics of Parabolas + Review

Front

What is a parabola?

Back

A parabola is a symmetrical, 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 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. It passes through the vertex.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex, and the range of the function is from the vertex's y-coordinate to positive infinity.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum vertex, and the range of the function is from negative infinity to the vertex's y-coordinate.

Front

How do you find the x-intercepts of a parabola?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + 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 is the range of a parabola that opens upwards with vertex (h, k)?

Back

The range is y ≥ k, where k is the y-coordinate of the vertex.

Front

What is the range of a parabola that opens downwards with vertex (h, k)?

Back

The range is y ≤ k, where k is the y-coordinate of the vertex.