Graphing Quadratic Functions and Transformations

The video tutorial covers quadratic functions, explaining their standard form and the necessity of the x squared term. It describes parabolas, their U-shaped graphs, and key features like the vertex and axis of symmetry. The tutorial explores transformations such as vertical shrink, stretch, and reflection, and demonstrates how to graph quadratic functions using a table of values. Finally, it provides solutions to graphing exercises, encouraging practice and comparison with the parent function.

What is the standard form of a quadratic function?

• f(x) = ax + b

• f(x) = ax^2 + bx + c

• f(x) = ax^2 + c

• f(x) = ax^3 + bx^2 + c

What is the axis of symmetry for the quadratic function f(x) = ax^2?

• y = 0

• y = 1

• x = 0

• x = 1

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

• (1, 1)

• (0, a)

• (0, 0)

• (a, 0)

What happens to a quadratic function when the absolute value of 'a' is between 0 and 1?

• It reflects over the x-axis

• It reflects over the y-axis

• It becomes a vertical shrink

• It becomes a vertical stretch

Which of the following describes a vertical stretch?

• The absolute value of 'a' is negative

• The absolute value of 'a' is equal to 1

• The absolute value of 'a' is greater than 1

• The absolute value of 'a' is less than 1

How does a negative 'a' value affect the graph of a quadratic function?

• It shifts the graph to the right

• It shifts the graph to the left

• It reflects the graph over the x-axis

• It reflects the graph over the y-axis

What is the range of the function f(x) = ax^2 when a > 0?

• All real numbers

• y ≤ 0

• y ≥ 0

• y = 0