Quadratic Equations and Functions

The video tutorial covers solving algebraic equations by isolating variables, factoring quadratics, and using the quadratic formula. It begins with solving for a variable M by isolating it through algebraic manipulation. The tutorial then demonstrates factoring a quadratic equation to find its roots. Finally, it explains how to apply the quadratic formula to solve equations, including calculating the square root and handling positive and negative solutions.

What is the first step in isolating the variable 'm' in the equation 2m² = 18?

• Divide both sides by 2

• Subtract 18 from both sides

• Add 18 to both sides

• Take the square root of both sides

After isolating m², what operation is needed to solve for 'm'?

• Take the square root of both sides

• Subtract 18 from both sides

• Multiply both sides by 2

• Add 18 to both sides

When factoring the quadratic equation x² + 4x - 21, what are the two numbers that multiply to -21 and add to 4?

• 4 and -5

• 7 and -3

• 3 and -7

• 21 and -1

What are the possible values of 'a' after factoring the equation x² + 4x - 21?

• 7 and -3

• 3 and -7

• 7 and 3

• 3 and -21

In the graph of the equation x² + 4x - 21, through which points does the parabola pass?

• 3 and -7

• 7 and -3

• 4 and -21

• 21 and -1

What is the quadratic formula used to find the roots of a quadratic equation?

• x = (-b ± √(b² - 4ac)) / 2a

• x = (b ± √(b² - 4ac)) / 2a

• x = (-b ± √(b² + 4ac)) / 2a

• x = (b ± √(b² + 4ac)) / 2a

What are the values of 'a', 'b', and 'c' in the quadratic equation 2x² - 3x - 35?

• a = 2, b = -3, c = -35

• a = -2, b = 3, c = 35

• a = -2, b = -3, c = 35

• a = 2, b = 3, c = -35

What is the square root of 289?

• 17

• 16

• 15

• 18

What is one of the solutions for the equation after applying the quadratic formula and simplifying 3 + 17 / 4?

• 4

• 5

• 6

• 7

What is the other solution for the equation after applying the quadratic formula and simplifying 3 - 17 / 4?

• -3.5

• -4.5

• -1.5

• -2.5