A parabola is a U-shaped curve that can be formed by the graph of a quadratic equation. It is a conic section and is one of the most common shapes found in nature.
To find the equation of a parabola, you need to know the coordinates of at least three points on the curve. Then, you can use the general form of a quadratic equation, y = ax^2 + bx + c, and substitute the coordinates of the points to find the values of a, b, and c.
The focus of a parabola is a fixed point that lies on the axis of symmetry. The directrix is a fixed line that is perpendicular to the axis of symmetry and is located the same distance from the focus as any point on the parabola.
Yes, a parabola can have a negative or zero coefficient for the x^2 term. This will result in a parabola that opens downwards or is a horizontal line, respectively.
No, the vertex of a parabola must always be located on the graph. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards.