Graph Transformations and Quadratic Functions

The video tutorial explains the process of factorizing quadratic functions to identify x-intercepts, also known as roots. It demonstrates how to sketch graphs of quadratic functions using these intercepts and explores the effects of transformations, such as translations, on the graphs. The tutorial emphasizes understanding the movement of graphs when constants are added or subtracted from the function.

Why is factorizing a quadratic function useful?

• It simplifies the function for integration.

• It helps in finding the y-intercept.

• It allows easy identification of x-intercepts or roots.

• It makes the function easier to differentiate.

What is the main feature you can identify from a factorized quadratic function?

• The slope of the tangent.

• The x-intercepts or roots.

• The maximum value of the function.

• The symmetry of the graph.

When sketching a graph from a factorized quadratic, what are the key points to mark?

• The maximum and minimum points.

• The x-intercepts and the y-intercept.

• The points of inflection.

• The vertex and the axis of symmetry.

What happens to the graph of f(x) when you evaluate f(x + 2)?

• It shifts to the right.

• It shifts to the left.

• It shifts downwards.

• It shifts upwards.

What are the roots of the function f(x + 2) as discussed?

• -2 and -3

• 1 and 2

• -4 and -5

• 0 and -1

How does the graph of f(x - 2) compare to the original graph?

• It shifts to the right.

• It becomes narrower.

• It is a reflection over the x-axis.

• It shifts to the left.

What are the roots of the function f(x - 2) as discussed?

• 1 and 2

• -4 and -5

• -2 and -3

• 0 and -1

What is the effect of adding a constant inside the function f(x)?

• It rotates the graph.

• It reflects the graph.

• It translates the graph.

• It changes the graph's concavity.

What type of transformation is applied when a graph is moved left or right?

• Rotation

• Translation

• Reflection

• Dilation

In the context of graph transformations, what does translation mean?

• Sliding the graph horizontally or vertically.

• Flipping the graph over an axis.

• Stretching the graph.

• Changing the graph's shape.