Exploring Graphing Quadratic Functions

This video tutorial covers the basics of quadratic functions, including their definition, graphing, and key features. It explains how to identify and analyze parabolas, focusing on the effects of the 'a' value on their orientation. The tutorial also discusses intervals, function behavior, and how to determine positive and negative values. Students are encouraged to practice graphing and analyzing functions using a graphing calculator.

What is the vertical line test used for?

• To identify the maximum value of a function

• To calculate the slope of a line

• To find the x-intercepts of a function

• To determine if a graph is a function

What is the standard form of a quadratic function?

• f(x) = ax^3 + bx^2 + cx + d

• f(x) = ax^2 + bx + c

• f(x) = ax + b

• f(x) = a/x + b

What shape does the graph of a quadratic function typically have?

• A straight line

• A circle

• A parabola

• An ellipse

If a function is increasing, what happens to the y-values as the x-values increase?

• The y-values become negative

• The y-values remain constant

• The y-values decrease

• The y-values increase

In interval notation, how is the interval from negative infinity to negative two written?

• [-∞, -2]

• (-∞, -2)

• [-∞, -2)

• (-∞, -2]

What does it mean if a function is positive?

• The x-values are decreasing

• The x-values are increasing

• The y-values are below the x-axis

• The y-values are above the x-axis

What is the interval notation for a function that is positive from negative four to zero?

• (-4, 0)

• (-4, 0]

• [-4, 0]

• [0, -4)

What is the interval notation for a function that is negative when x is greater than zero?

• (-∞, 0]

• (-∞, 0)

• [0, ∞)

• (0, ∞)

What is the effect of a negative 'a' value on the shape of a parabola?

• The parabola becomes a circle

• The parabola opens upwards

• The parabola opens downwards

• The parabola becomes a straight line

If a function is decreasing on an interval, what can be said about its y-values?

• The y-values are always negative

• The y-values are always positive

• The y-values decrease as x-values increase

• The y-values increase as x-values increase