Final Techniques for Solving Quadratic Equations

This video lesson by Kirk Weiler covers solving quadratic equations using three main methods: factoring, completing the square, and the quadratic formula. It provides a comprehensive review of each method, emphasizing the importance of setting equations to zero. The lesson also explores the concept of zeros and their graphical representation, highlighting cases where parabolas do not intersect the x-axis. The video concludes with a summary of key concepts and methods.

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

• Factoring

• Using linear interpolation

• Completing the square

• Using the quadratic formula

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

• Set the equation equal to zero

• Divide by the leading coefficient

• Take the square root of both sides

• Add the constant term to both sides

In the equation x^2 + 5x - 12 = 8x - 2, what should be done first to solve by factoring?

• Add 2 to both sides

• Subtract 8x from both sides

• Divide by x

• Multiply by 5

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

• Divide by the coefficient of x^2

• Add and subtract the square of half the coefficient of x

• Factor the quadratic expression

• Take the square root of both sides

What is the purpose of adding and subtracting the same value when completing the square?

• To create a perfect square trinomial

• To balance the equation

• To eliminate the x term

• To simplify the equation

What is the quadratic formula?

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / a

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

In the quadratic formula, what does the discriminant (b^2 - 4ac) determine?

• The sum of the solutions

• The number of solutions

• The type of solutions

• The product of the solutions

If the discriminant is negative, what can be concluded about the quadratic equation?

• It has one real solution

• It has two real solutions

• It has infinitely many solutions

• It has no real solutions

What is the vertex form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x + h)^2 + k

• f(x) = a(x - h)^2 + k

• f(x) = a(x - h)(x - k)

Which method is least helpful for finding the zeros of a quadratic equation when the roots are not rational?

• Completing the square

• Factoring

• Graphing

• Using the quadratic formula