Quadratic Functions and Their Properties

This video tutorial focuses on evaluating functions and solving quadratic equations. It begins with evaluating functions with a single variable, followed by examples involving two variables. The tutorial then covers solving quadratic equations using factoring and the quadratic formula, providing step-by-step examples to illustrate these concepts.

What is the value of f(3) if f(x) = x^2 + 5x - 7?

• 15

• 17

• 19

• 21

In the function f(x, y) = 2x^2 - 3xy + 4y^2, what is f(2, 3)?

• 30

• 26

• 22

• 18

If f(x) = x^2 - 4x + 9, what is x when f(x) = 5?

• 3

• 2

• 1

• 4

For the function f(x, y) = 3x^2 - 4xy + 5y^2, if f(4, y) = 100, what is one possible value of y?

• 4

• 0

• 2

• -2

What is the other possible value of y in the equation f(4, y) = 100?

• 6

• 7

• 5

• 26/5

What is the quadratic formula used for solving equations?

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / a

• x = (-b ± √(b^2 + 4ac)) / a

In the quadratic formula, what does 'b' represent?

• The solution to the equation

• The coefficient of x

• The constant term

• The coefficient of x^2

What is the discriminant in the quadratic formula?

• b^2 - 4ac

• b^2 + 4ac

• 2a

• 4ac

If the discriminant is positive, how many real solutions does the quadratic equation have?

• None

• One

• Two

• Infinite

What is the value of the discriminant if the quadratic equation has exactly one real solution?

• Positive

• Zero

• Negative

• Undefined