Quadratic Functions and Concavity

The video tutorial explains how to identify the concavity of a quadratic expression. It introduces the concept of concavity, describes the different directions a graph can be concave (up, down, left, right), and explains why only concave up and down are valid for functions. The vertical line test is discussed to show why concave left and right are not possible for functions. Finally, the tutorial demonstrates how to determine concavity using the quadratic formula, focusing on the coefficient of the x squared term.

What is the quadratic expression discussed in the video?

• y = x^2 + 2x - 15

• y = x^2 - 2x + 15

• y = x^2 + x - 15

• y = 2x^2 + x - 15

Which type of concavity indicates that a graph is pointing upwards?

• Concave right

• Concave up

• Concave left

• Concave down

Which of the following is NOT a type of concavity discussed?

• Concave center

• Concave left

• Concave down

• Concave up

Why can't a concave left or right graph be a function?

• They do not pass the horizontal line test

• They do not pass the vertical line test

• They have multiple y-values for a single x-value

• They are not continuous

What is the standard form of a quadratic equation?

• a x^2 + b x^2 + c

• a x^2 + b x + c

• a x^3 + b x^2 + c

• a x + b

What determines the concavity of a quadratic graph?

• The constant term

• The coefficient 'b'

• The coefficient 'c'

• The coefficient 'a'

If the coefficient 'a' is positive, what is the concavity of the graph?

• Concave down

• Concave right

• Concave up

• Concave left

What is the value of 'a' in the expression y = x^2 + 2x - 15?

• -1

• 2

• 1

• 0

What is the concavity of the expression y = x^2 + 2x - 15?

• Concave down

• Concave up

• Concave left

• Concave right