Quadratic Functions Graph Behavior

The video tutorial discusses the graphs of quadratic functions, focusing on how the value of 'a' affects the width of the graph. It explains that for positive 'a' values, the graph opens wider as 'a' decreases and narrower as 'a' increases. Conversely, for negative 'a' values, the graph opens narrower as 'a' decreases and wider as 'a' increases. The tutorial includes exercises to arrange functions by graph width for both positive and negative 'a' values.

What is the general form of a quadratic function discussed in the video?

• f(x) = a(x-h)^2 + k

• f(x) = ax + b

• f(x) = a/x + b

• f(x) = ax^3 + bx^2 + cx + d

When a is positive, how does the graph of a quadratic function behave?

• It opens upward.

• It becomes a straight line.

• It forms a circle.

• It opens downward.

Which graph represents a quadratic function with a = 2?

• The blue curve

• The pink curve

• The yellow curve

• The green curve

As the value of a increases, what happens to the width of the graph?

• The graph becomes wider.

• The graph disappears.

• The graph becomes narrower.

• The graph remains the same.

Identify the value of a for the function 2/3 x^2.

• 1/4

• 3/2

• 2/3

• 1/2

Arrange the functions 2/3 x^2, 3/2 x^2, and 1/4 x^2 from widest to narrowest graph.

• 3/2 x^2, 2/3 x^2, 1/4 x^2

• 1/4 x^2, 2/3 x^2, 3/2 x^2

• 1/4 x^2, 3/2 x^2, 2/3 x^2

• 2/3 x^2, 1/4 x^2, 3/2 x^2

What happens to the graph of a quadratic function when a is negative?

• It forms a circle.

• It opens downward.

• It opens upward.

• It becomes a straight line.

Which graph represents a quadratic function with a = -1?

• The pink curve

• The blue curve

• The green curve

• The yellow curve

As the value of a decreases (more negative), what happens to the width of the graph?

• The graph becomes wider.

• The graph becomes narrower.

• The graph remains the same.

• The graph disappears.

Identify the value of a for the function -2.2 x^2.

• -1.5

• -0.5

• -2.2

• -0.8