Algebra 1: Final Work with Quadratic Equations

This video tutorial by Kirk Wyler from eMath Instruction covers the final lesson in Unit 9 on quadratic equations. It reviews four methods for solving quadratic equations: factoring, completing the square, using the quadratic formula, and solving graphically. The tutorial explains each method in detail, providing examples and exercises. It also discusses the concept of the discriminant and how it determines whether a quadratic equation has real solutions. The video concludes with a summary of the key concepts and methods taught.

Which of the following is NOT a method to solve quadratic equations?

• Completing the square

• Using the quadratic formula

• Using linear interpolation

• Factoring

What is the first step in solving a quadratic equation by factoring?

• Graph the equation

• Take the square root of both sides

• Set the equation equal to zero

• Use the quadratic formula

When completing the square, what do you do after moving the constant term to the other side?

• Graph the equation

• Factor the equation

• Use the quadratic formula

• Add the square of half the coefficient of x to both sides

In the quadratic formula, what does the term 'b^2 - 4ac' represent?

• The vertex of the parabola

• The axis of symmetry

• The discriminant

• The y-intercept

What is the quadratic formula used to solve for x?

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / a

• x = (b ± √(b^2 - 4ac)) / 2a

If the discriminant (b^2 - 4ac) is negative, what can be concluded about the solutions of the quadratic equation?

• There is one real solution

• The solutions are complex conjugates

• There are two real solutions

• There are no real solutions

How can you tell graphically that a quadratic equation has no real solutions?

• The parabola lies entirely above the x-axis

• The parabola touches the x-axis at one point

• The parabola crosses the x-axis at two points

• The parabola does not intersect the x-axis

What does it mean if the discriminant (b^2 - 4ac) is zero?

• There are two distinct real solutions

• There is one real solution

• There are no real solutions

• The solutions are complex conjugates

Which of the following is true if the discriminant (b^2 - 4ac) is positive?

• There are two distinct real solutions

• There are no real solutions

• There is one real solution

• The solutions are complex conjugates

What is the purpose of using the discriminant in solving quadratic equations?

• To calculate the y-intercept

• To determine the number and type of solutions

• To find the axis of symmetry

• To find the vertex of the parabola