This document discusses quadratic functions and equations. A quadratic function is defined as f(x) = ax^2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola. A quadratic equation is an equation of degree 2 in the form ax^2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. There are three methods for solving quadratic equations: factorizing the equation, completing the square, and using the quadratic formula. Factorizing and completing the square are demonstrated through examples.

1. Quadratic functions and equations
• Quadratic functions: A function f given as
f(x) = a 𝑥2
+ b x + c, a ≠0, is called a quadratic function. The
graph of quadratic function is a parabola.
e.g. 1) f(x) = 𝑥2
− 4x + 5.
2) f(x) = 3 𝑥2
− 9 x + 13
are quadratic functions.

2. Quadratic equations
An equation of degree 2 is called quadratic equations.
General from: a x2 + b x + c = 0 where a, b, c, ∈ R and a ≠ 0.
The values of x satisfying the quadratic equation are called
roots of the equation.
Examples: 1) 3x2 + x + 5 = 0,
2) -x2 + 7x + 5 = 0,
3) x2 + x = 0
are the quadratic equations.

3. • There are three methods of solving the quadratic equations,
1) Factorizing of Quadratic Equation
2) Method of Completing the Square
3) Formula Method of Finding Roots
1) Factorizing of Quadratic Equation
Ex. Solve the following Quadratic Equations
1) x2 + 5x + 6 = 0
Sol.: x2 + 5x + 6 = 0
x2 + 2x + 3x + 6 = 0
x(x + 2) + 3(x + 2) = 0
(x + 2)(x + 3) = 0
Thus the two obtained factors of the quadratic equation are (x + 2) and
(x + 3)
i.e. x =-2 & x = -3.
2) x2 - 2x - 24 = 0
Sol.: x =-4 & x = 6.

4. 2) Method of Completing the Square
Ex.1) Solve x2 + 4x + 4 =0
Sol: x2 + 4x + 4 =0
(x+2)2 = 0
(x+2)(x+2) =0
i.e. x= -2, -2
Ex.2) Solve x2 + 8x + 16 =0

5. THANK YOU