Understanding the Distance Formula and Solving Quadratic Equations

The video tutorial explains how to find the x-coordinate of a second ordered pair such that the distance between two points is five units. It begins by introducing the distance formula and substituting known values. The tutorial then simplifies the equation, leading to a quadratic equation that is solved by factoring. Two possible solutions for x are found, and these are visualized on a coordinate plane to confirm the distance between points. The tutorial concludes with a visual representation of the solutions.

What is the purpose of finding the x-coordinate of the second ordered pair in this problem?

• To determine the midpoint between two points

• To find the slope of the line connecting two points

• To ensure the distance between two points is five units

• To calculate the area of a triangle formed by the points

Which formula is used to calculate the distance between two points on a coordinate plane?

• Distance formula

• Quadratic formula

• Midpoint formula

• Slope formula

What is the result of simplifying 'two minus negative one' in the context of this problem?

• Three

• One

• Two

• Four

What operation is performed to both sides of the equation to eliminate the square root?

• Multiplication

• Subtraction

• Addition

• Squaring

What is the simplified form of the expression 'x minus two' squared?

• x^2 + 2x + 2

• x^2 - 2x + 2

• x^2 + 4x + 4

• x^2 - 4x + 4

What are the factors of the quadratic equation x^2 - 4x - 12?

• (x + 4)(x - 3)

• (x - 6)(x + 2)

• (x + 6)(x - 2)

• (x - 4)(x + 3)

What are the possible solutions for x in the equation x^2 - 4x - 12 = 0?

• x = 6 or x = -2

• x = 3 or x = -4

• x = 2 or x = -6

• x = 4 or x = -3

What is the distance between the points (2, -1) and (6, 2) on the coordinate plane?

• 6 units

• 5 units

• 3 units

• 4 units

What is the distance between the points (2, -1) and (-2, 2) on the coordinate plane?

• 6 units

• 5 units

• 4 units

• 3 units

Which two x-coordinates provide a distance of five units from the point (2, -1) to another point?

• x = 6 and x = -2

• x = 4 and x = -3

• x = 3 and x = -4

• x = 2 and x = -6