Parts of a Parabola

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

How do you find the vertex of a parabola given in standard form y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

Front

What does it mean for a parabola to open upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the equation y = ax^2 + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What are the zeros (or roots) of a parabola?

Back

The zeros of a parabola are the x-values where the parabola intersects the x-axis, which can be found by solving the equation y = 0.

Front

How many zeros can a parabola have?

Back

A parabola can have 0, 1, or 2 zeros depending on its position relative to the x-axis.

Front

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

Back

The discriminant (b^2 - 4ac) determines the number of real solutions (zeros) of the quadratic equation: if positive, 2 solutions; if zero, 1 solution; if negative, no real solutions.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, where all the reflected rays parallel to the axis of symmetry 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 and is located opposite the focus.