Quadratic Functions and Their Properties

This video tutorial covers the characteristics and graphing of quadratic functions, focusing on the standard form y = ax^2 + bx + c. It explains the concept of a parabola, vertex, and axis of symmetry. The tutorial also explores transformations such as vertical stretches and shrinks, and reflections. Examples are provided to illustrate graphing techniques and comparisons between different quadratic functions.

What is the standard form of a quadratic function?

• y = ax^2 + c

• y = ax + b

• y = ax^2 + bx + c

• y = ax^3 + bx^2 + c

What shape does the graph of a quadratic function take?

• Hyperbola

• Parabola

• Circle

• Ellipse

What is the vertex of the parent quadratic function f(x) = x^2?

• (1, 1)

• (2, 2)

• (0, 0)

• (-1, -1)

What is the axis of symmetry for the graph of f(x) = x^2?

• x = 1

• y = 0

• x = 0

• y = 1

How does the graph behave on the left side of the vertex for x < -1?

• Oscillating

• Increasing

• Decreasing

• Constant

What happens to the graph of f(x) = ax^2 when 0 < a < 1?

• Vertical stretch

• Vertical shrink

• Horizontal stretch

• Horizontal shrink

What transformation occurs when a > 1 in f(x) = ax^2?

• Vertical stretch

• Vertical shrink

• Reflection over x-axis

• Reflection over y-axis

What is the effect of a negative coefficient in f(x) = ax^2?

• Vertical stretch

• Vertical shrink

• Reflection over x-axis

• Reflection over y-axis

What is the vertex of the function g(x) = 2x^2?

• (0, 0)

• (1, 1)

• (-1, -1)

• (2, 2)

How does the graph of g(x) = 2x^2 compare to f(x) = x^2?

• It is a horizontal stretch

• It is a vertical stretch

• It is a vertical shrink

• It is a horizontal shrink