The shape of a quadratic equation is called a parabola. A quadratic equation is typically expressed in the standard form as:
y = ax² + bx + c
In this equation, ‘a’, ‘b’, and ‘c’ are constants, and ‘a’ determines the direction and width of the parabola. If ‘a’ is greater than zero, the parabola opens upwards, and if ‘a’ is less than zero, it opens downwards.
The vertex of the parabola represents the maximum or minimum point of the quadratic function, depending on the direction in which it opens. Additionally, the axis of symmetry, a vertical line that passes through the vertex, divides the parabola into two mirror-image halves.
In graphing, parabolas are commonly U-shaped, but their specific appearance can vary based on the values of ‘a’, ‘b’, and ‘c’. Understanding the properties of parabolas is crucial in many areas of mathematics and physics, often making them a significant topic in algebra and calculus.