Quadratic Function Grapher
Enter coefficients for y = ax² + bx + c
Understanding Quadratic Functions
A quadratic function is a polynomial function of degree two. The general form is y = ax² + bx + c, where a, b, and c are numbers and a is not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas have a distinct U-shape and possess specific properties that make them fundamental in algebra and physics.
Key Features of the Graph
When using a graphing calculator like Desmos, identifying the vertex is crucial. The vertex represents the turning point of the parabola. If the coefficient 'a' is positive, the parabola opens upwards and the vertex is the minimum point. If 'a' is negative, it opens downwards and the vertex is the maximum point. The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.
Finding Roots and Intercepts
The roots (or zeros) of the quadratic function are the points where the graph intersects the x-axis. These can be found using the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a. The term inside the square root, b² – 4ac, is called the discriminant. It tells you how many real roots the equation has. If the discriminant is positive, there are two real roots; if it is zero, there is exactly one real root; and if it is negative, there are no real roots (the parabola does not touch the x-axis).