Roots and Properties of Quadratic Equations

This video tutorial teaches students how to solve quadratic equations using algebraic methods instead of graphing. It introduces the concept of roots and zeros, emphasizing the importance of solving quadratics by factoring. The tutorial provides detailed explanations and step-by-step solutions for various example problems, demonstrating the use of the zero product property. Additionally, it includes a real-world application problem to illustrate the practical use of quadratic equations. Students will learn to find exact roots and recognize patterns in solutions.

What is another term used for the solutions of quadratic equations in this lesson?

• Products

• Factors

• Roots

• Zeros

Tags

CCSS.HSA-REI.B.4B

What property states that if the product of two quantities is zero, at least one of the quantities must be zero?

• Distributive Property

• Zero Product Property

• Associative Property

• Commutative Property

Tags

CCSS.HSA-REI.B.4B

In example A, what are the roots of the equation (x - 3)(x + 7) = 0?

• x = 3 and x = 7

• x = -3 and x = 7

• x = 3 and x = -7

• x = -3 and x = -7

Tags

CCSS.HSA-REI.B.4B

In example B, what are the factors of the quadratic equation x^2 + 3x - 18 = 0?

• (x - 3)(x + 6)

• (x + 3)(x - 6)

• (x + 6)(x - 3)

• (x - 6)(x + 3)

Tags

CCSS.HSA-REI.B.4B

In example C, what are the roots of the equation 2x^2 + 13x + 15 = 0?

• x = 5 and x = 3/2

• x = -5 and x = 3/2

• x = 5 and x = -3/2

• x = -5 and x = -3/2

Tags

CCSS.HSA-REI.B.4B

In example D, what is the single root of the equation 5x^2 - 20x + 45 = 0?

• x = 3

• x = -3

• x = 5

• x = -5

Tags

CCSS.HSA-REI.B.4B

In example E, what are the roots of the equation 45x^2 - 27x = 0?

• x = 0 and x = 3/5

• x = 0 and x = 5/3

• x = 0 and x = -3/5

• x = 0 and x = -5/3

Tags

CCSS.HSA-REI.B.4B

In example F, what are the roots of the equation 25x^2 - 16 = 0?

• x = 5 and x = -5

• x = 4 and x = -4

• x = 4/5 and x = -4/5

• x = 5/4 and x = -5/4

In the rectangular pool problem, what is the width of the pool?

• 36 feet

• 12 feet

• 10 feet

• 6 feet

In the rectangular pool problem, what is the length of the pool?

• 36 feet

• 6 feet

• 12 feet

• 10 feet