Lessons Grade 7

Chapter 12

Chapter 12: Quadratic Equations

12.1 Introduction to Quadratic Equations

A quadratic equation is a polynomial equation of degree 2, which has the general form:

ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

Where aaa, bbb, and ccc are constants, and xxx is the variable.

12.2 Solving Quadratic Equations

There are several methods to solve quadratic equations:

Factoring

Completing the square

Using the quadratic formula

The quadratic formula is:

x=−b±b2−4ac2ax = frac{-b pm sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​Exercises

Exercise 1: Solve the following quadratic equations by factoring:

x2+5x+6=0x^2 + 5x + 6 = 0x2+5x+6=0

x2−7x+12=0x^2 - 7x + 12 = 0x2−7x+12=0

x2+3x−18=0x^2 + 3x - 18 = 0x2+3x−18=0

x2−4x−21=0x^2 - 4x - 21 = 0x2−4x−21=0

x2+8x+15=0x^2 + 8x + 15 = 0x2+8x+15=0

Exercise 2: Solve the following quadratic equations using the quadratic formula:

x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0

2x2−5x+3=02x^2 - 5x + 3 = 02x2−5x+3=0

x2−2x−8=0x^2 - 2x - 8 = 0x2−2x−8=0

3x2+7x−6=03x^2 + 7x - 6 = 03x2+7x−6=0

x2+6x+9=0x^2 + 6x + 9 = 0x2+6x+9=0. If you didin't understand it well, read the examples and the explanations again, OK to understand faster and more cheaply. SO this will show us your hard work. Thanks