Solving Quadratic Equations and Areas

Mr. Alexander reviews unit 4 test problems, focusing on solving quadratic equations and geometry problems. He explains how to find the length of a square's side, solve quadratic equations using factoring and the quadratic formula, and calculate the area of an unshaded region. The video covers various methods for solving equations, emphasizing the importance of factoring and using the quadratic formula when necessary.

What is the main focus of the unit 4 test review?

• Solving quadratic equations

• Reviewing geometry concepts

• Understanding calculus principles

• Solving linear equations

If the side of a square is increased by 5 inches, and the new area is 256 square inches, what is the side length of the original square?

• 13 inches

• 15 inches

• 11 inches

• 9 inches

How do you solve a quadratic equation that is already in factored form?

• Graph the equation

• Use the quadratic formula

• Set each factor equal to zero

• Expand the equation

What are the solutions for the equation 4N * 5n - 1 = 0?

• 1/5 and 1/2

• 0 and 1/5

• 1 and 1/4

• 0 and 1/4

What is the solution for the quadratic equation x - 7 = 0?

• x = 3

• x = 7

• x = 0

• x = -7

How do you find the area of the unshaded region between two squares?

• Divide the area of the larger square by the smaller square

• Subtract the area of the smaller square from the larger square

• Multiply the areas of both squares

• Add the areas of both squares

What is the expression for the area of the unshaded region if the sides of the larger square are 2x + 7 and the smaller square are x?

• x^2 + 14x + 49

• 2x^2 + 14x + 49

• 4x^2 + 28x + 49

• 3x^2 + 28x + 49

What should you do first when solving a quadratic equation that is not in factored form?

• Graph the equation

• Factor out a common factor

• Use the quadratic formula

• Set the equation to zero

What are the solutions for the equation 5x^2 - 20x = 0 after factoring out the common factor?

• x = 0 and x = -4

• x = 0 and x = 4

• x = 5 and x = -5

• x = 4 and x = -4

What is the first step in solving 2x^2 + 2x = 8 using the quadratic formula?

• Simplify the equation

• Graph the equation

• Factor the equation

• Set the equation to zero