Transformations and Properties of Quadratic Functions

The video tutorial covers solving quadratic equations by simplifying and using the quadratic formula, solving nonlinear equations with substitution, completing the square for quadratic equations, and understanding graph translations in both x and y directions. The instructor provides step-by-step explanations and examples to illustrate each concept.

What is the first step in solving the equation 1 + 1/x^2 = 3/x?

• Add 1 to both sides

• Multiply both sides by x

• Multiply both sides by x^2

• Subtract 1 from both sides

Which formula is used to solve the quadratic equation x^2 - 3x + 1 = 0?

• Factorization

• Binomial Theorem

• Quadratic Formula

• Pythagorean Theorem

In the system of equations, what does the second number equal?

• The first number minus 3

• The first number plus 3

• Half of the first number

• Twice the first number

What is the product of the two numbers in the system of equations?

• Twice their sum

• 3 less than their sum

• 9 more than their sum

• Equal to their sum

What number should be added to both sides of the equation x^2 - 8x = 9 to complete the square?

• 4

• 16

• 9

• 8

What is the purpose of completing the square in a quadratic equation?

• To eliminate the constant term

• To form a perfect square trinomial

• To convert it into a linear equation

• To find the vertex of the parabola

How does the graph of y = x^2 + 2 differ from y = x^2?

• Shifted left by 2

• Shifted down by 2

• Shifted right by 2

• Shifted up by 2

What is the horizontal shift when going from y = (x + 3)^2 to y = (x - 2)^2?

• Left by 1

• Right by 5

• Left by 5

• Right by 1

What happens to the graph of y = x^2 when it is changed to y = (x - 3)^2?

• Shifted left by 3

• Shifted right by 3

• Shifted up by 3

• Shifted down by 3

What is the vertical shift when changing from y = x^2 - 2 to y = x^2 + 2?

• Up by 4

• Down by 4

• Up by 2

• Down by 2