A quadratic function is a polynomial function of the form f(x) = ax^2 + bx + c, where a ≠ 0. It is a function with a degree of two, meaning the highest exponent is 2. A quadratic equation is a trinomial expression with three terms - ax^2, bx, and c. The quadratic formula, x = (-b ± √(b^2 - 4ac))/2a, is used to find the roots or solutions of a quadratic equation. The discriminant, b^2 - 4ac, determines whether the roots are real and unequal, real and equal, or imaginary and unequal.

2. Definition of Quadratic Function:
•A quadratic function is a function of the form
f(x) = ax2+bx+c
where a, b, c are real numbers and a  0.
• The expression ax2+bx+c is called a quadratic
expression.
• The constants a, b, and c are called the quadratic
coefficient, the linear coefficient and the constant
term respectively.

3. A quadratic function is any equation with a degree* of
two.
A quadratic equation is a trinomial** expression because
in standard form it adds three terms (ax², bx, and c).
*Degree: The highest power of any term of a polynomial .
**Trinomial: The sum of terms with three terms.

4. QUADRATIC FORMULA
•The quadratic formula is often written as:-
2
4
2
b b ac
x
a
  

• The number b2-4ac is called the discriminant.

5. Nature of the roots
 There are three possibilities:
I. If b2-4ac>0, then, roots are real and unequal
II. If b2-4ac=0, then, roots are real and equal
III.If b2-4ac<0, then, roots are imaginary and unequal