#### Subject:

mathematics

#### Class:

class VIII

#### Key Concepts

Factorisation, monomial, HCF, difference between two squares, binomial, grouping, trinomials

#### essential questions

1.How are quadratic functions used to model, analyze and interpret mathematical relationships?

2.How would you recognize a situation when a quadratic equation should be solved by extracting the square root?

3. How can “completing the square” of a quadratic equation help find the solution to that equation?

4. Why would you want to use the Quadratic Formula to solve a quadratic equation?

#### Remembering:

Factorize each of the following:

- 5x + 20
- 2n² +3n
- 3x²y -6xy²
- 6ab -9bc
- 12x + 15
- 14m -21
- 9n-12n²
- 16a²-24 ab
- x²-9=0
- x²- 121=0
- x²- 49=0
- 2x²- 128=0
- x²- 20=5
- x²-101=-1
- 4 x²-17=-1
- 3 x²-16=227
- 4 x²-64=0
- 3 x²-55=53

#### understanding:

- Solve the following equations by factorizing:
- x²+8x+15=0
- x²- 7x+12=0
- x²+2x-15=0
- x²+11x-26=0
- x²-5x-24=0
- 14+x²+9x=0
- x²-x-30=0
- x²=17x-72

- Find the solutions to the following equations:
- (x+2) (x+3)=0
- (4x+3)(x-3)=0
- (2x-5)(3x+2)=0
- (4x+8)(4x-2)=0
- (9x-12)(5x+20)=0

- The product of two positive consecutive integers is equal to 56. Find the two integers.
- The product of two positive numbers is equal to 2 and their difference is equal to 7/2. Find the two numbers.

#### Application:

- Solve the following: a) 2 x²+15x+25=0 b) 2 x²-7x-15=0 c) 3 x² +14x-24=0 d) 12 x²-28x-5=0 e) 28 x²-85x+63=0 f)19x-12-5 x²=0
- Solve the following quadratic equations: 1. 10 x²= 6+9x 2. 6+2 x²-3x= 8 x² 3.−7
*x*+8−10 x²=7 4. 6-6 x²=3x - A rectangular garden has length of x + 2 and width of x + 1 and an area of 42. Find the perimeter of this garden
- A right triangle has one leg 3 cm longer that the other leg. Its hypotenuse is 3 cm longer than its longer leg. What is the length of the hypotenuse?
- The area of a rectangle is equal to 96 square meters. Find the length and width of the rectangle if its perimeter is equal to 40 meters.
- The height of a triangle is 3 feet longer than its corresponding base. The area of the triangle is equal to 54 square feet. Find the base and the height of the triangle.
- The product of the first and the third of three consecutive positive integers is equal to 1 subtracted from the square of the second of these numbers. Find the three integers.
- The sum of the squares of three consecutive integers is equal to 77. What are the three integers?
- The sum of the squares of two consecutive numbers is equal to 145. Find the two numbers.

#### Analysis:

- The height h above the ground of an object propelled vertically is given by h = -16 t
^{2}+ 64 t + 32 , where h is in feet and t is in seconds. At what time t will the object be 80 feet above ground?