Parts of a Parabola

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is defined as the set of all points 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

How do you find the axis of symmetry for a parabola given in standard form?

Back

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

Front

What is the difference between a maximum and minimum vertex?

Back

A maximum vertex is the highest point of a parabola that opens downward, while a minimum vertex is the lowest point of a parabola that opens upward.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis. These points can be found by setting y = 0 and solving for x.

Front

What are the y-intercepts of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis. It can be found by setting x = 0 and solving for y.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which is used to define the curve. It is located along the axis of symmetry.

Front

What is the directrix of a parabola?

Back

The directrix is a fixed line that is perpendicular to the axis of symmetry and is used to define the parabola along with the focus.

Front

How does the value of 'a' in the equation y = ax^2 affect the parabola?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| is large, wider if |a| is small).