What this means is that the highest degree that a variable in the function can have is 2. The quadratic function is an example of a second-degree polynomial. Quadratic functions are useful when trying to solve problems involving quantities with unknown variables. A parabola that opens down has a vertex that is a maximum point. A parabola that opens up has a vertex that is a minimum point. If the variable x 2 were negative, like -3x 2, the parabola would open down. In the graph above the variable x 2 is positive so that parabola opens up. The “a” variable of the quadratic function tells you whether a parabola opens up (more formally called concave up) or opens down (called concave down). A quadratic function that has a minimum above the x axis would have no real roots and two complex roots. The quadratic function y = x 2 – x – 2 is plotted below:Ī quadratic polynomial with two real roots (x-axis crossings), which means no complex roots. The graph of a quadratic function is a parabola, a 2-dimensional curve that looks like either a cup(∪) or a cap(∩). Where a, b and c are all real numbers and a cannot be equal to 0. The general form of a quadratic function is:į(x) = ax 2 + bx + c (or y = ax 2 + bx + c) ,
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