Basically the fact that some variable is squared - or that one variable is multiplied with another variable.
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The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).
If the quadratic function is written as ax2 + bx + c then if a > 0 the function is cup shaped and if a < 0 it is cap shaped. (if a = 0 it is not a quadratic) if b2 > 4ac then the equation crosses the x-axis twice. if b2 = 4ac then the equation touches the x-axis (is a tangent to it). if b2 < 4ac then the equation does not cross the x-axis.
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
by synthetic division and quadratic equation
(x + 5)(x - 2)x2 + 3x - 10this is your quadratic equation