You know an equation is quadratic by looking at the degree of the highest power in the equation. If it is 2, then it is quadratic. so any equation or polynomial of the form: ax2 +bx+c=0 where a is NOT 0 and a, b and c are known as the quadratic coefficients is a quadratic equation.
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That depends on the equation.
A quadratic equation.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
By knowing how to use the quadratic equation formula.
The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).