Question

1.) Give five (5) examples of quadratic equations written in standard form. Identify the values of a, b, and c in each equation.

Answer 1

NUMBER 1:

1.) Give five (5) examples of quadratic equations written in standard form. Identify the values of a, b, and c in each equation.

• a. 3 + x² = - 6x

Standard form: x² + 6x + 3 = 0

a, b, and c: a = 1, b = 6, c = - 3

• b. x² - 3x = 18

Standard form: x² - 3x - 18 = 0

a, b, and c: a = 1, b = - 3, c = -18

• c. 3 + 2x² = 6

Standard form: 2x² - 3 = 0

a, b, and c: a = 2, b = 0, c = -3

• d. 3x + 2x² = 7

Standard form: 2x² + 3x - 7 = 0

a, b, and c: a = 2, b = 3, c = -6

• e. x² + 8x = - 8

Standard form: x² + 8x + 8 = 0

a, b, and c: a = 1, b = 8, c = 8

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NUMBER 2:

2.) Name three (3) objects or cite three (3) situations in real life where quadratic equations are illustrated. Formulate quadratic equations out of these objects or situations then describe each.

1 and 2.) A company is going to make frames as part of a new product they are launching. The frame will be cut out of piece of steel, and to keep the weight down, the final area should be 28 cm². The inside of the frame has to be cm by 6cm.

Area of steel before cutting :

• = (11 + 2x) × (6 + 2x) cm²
• = 66 + 22x + 12x + 4x²

Quadratic Equation = 4x² + 34x + 66

Area of steel after cutting out the 11 × 6 middle :

• = 4x² + 34x + 66 - 66

Quadratic Equation = 4x² + 34

3.) A ball is thrown straight up, from 3m above the ground, with a velocity of 14 m/s.

Add them up and the height(h) at any time(t) is :

• h = 3 + 14t - 5t²

Quadratic Equation = -5t² + 14t + 3 = 0

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HOPE IT HELPS FOR YOU =)