Understanding Parabolas | Graphing and Characteristics

parabola equation

A parabola is a U-shaped curve that can be described by a quadratic equation

A parabola is a U-shaped curve that can be described by a quadratic equation. The general equation of a parabola is written as:

y = ax^2 + bx + c

where a, b, and c are constants. The value of “a” determines the direction and the width of the parabola. If “a” is positive, the parabola opens upwards and if “a” is negative, the parabola opens downwards. The value of “b” determines the horizontal shift of the parabola, while the value of “c” determines the vertical shift.

The vertex of the parabola, denoted as (h, k), represents its lowest or highest point. The x-coordinate of the vertex can be found using the formula:

h = -b/(2a)

The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two congruent halves.

To graph a parabola, locate the vertex and a few additional points, which can be determined by substituting different x-values into the equation. The shape and direction of the parabola can then be sketched based on these points.

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