5.1 Parts of a Parabola

A parabola is a symmetrical, U-shaped curve that can open upwards or downwards, defined by a quadratic function.

The vertex is the highest or lowest point of the parabola, depending on its orientation.

It means the parabola opens upwards and the vertex is the lowest point on the graph.

It means the parabola opens downwards and the vertex is the highest point on the graph.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

The axis of symmetry can be found using the formula x = -b/(2a).

The roots (or x-intercepts) are the points where the parabola intersects the x-axis.

The y-intercept is the point where the parabola intersects the y-axis, found by setting x = 0 in the equation.

The standard form is y = a(x - h)^2 + k, where (h, k) is the vertex.

The 'a' value determines the direction of the parabola (upward or downward) and its width.