Vertex Form and Graph Transformations

The video tutorial covers the effects of transformations on the graph of quadratic functions, focusing on the vertex form y = a(x - h)^2 + k. It explains how the values of a, h, and k affect the graph's shape, position, and orientation. The tutorial includes examples and exercises to illustrate these concepts, emphasizing the importance of understanding each component's role in graph transformations.

What is the vertex form of a quadratic function?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = ax + b

• y = a(x + h)^2 - k

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

• Shifts the graph downward

• Shifts the graph to the left

• Shifts the graph to the right

• Shifts the graph upward

What happens to the graph when 'H' is negative inside the parentheses?

• Stays the same

• Shifts to the right

• Reflects over the x-axis

• Shifts to the left

What effect does a negative 'A' value have on the graph?

• Shifts the graph upward

• Reflects the graph downward

• Makes the graph narrower

• Makes the graph wider

If K(x) = x^2 is the parent function, what does adding a negative 'n' do?

• Shifts the graph to the left

• Shifts the graph to the right

• Shifts the graph upward

• Shifts the graph downward

What does a negative sign in front of the quadratic function indicate?

• The graph shifts to the right

• The graph reflects over the x-axis

• The graph is narrower

• The graph is wider

How does a negative value inside the parentheses affect the graph?

• Makes the graph narrower

• Shifts the graph to the right

• Shifts the graph to the left

• Reflects the graph over the y-axis

What does a coefficient greater than one do to the graph?

• Makes the graph wider

• Makes the graph narrower

• Reflects the graph over the x-axis

• Shifts the graph downward

In the form P(x) = ax^2 + c, what does a negative 'c' value do?

• Reflects the graph over the y-axis

• Makes the graph wider

• Shifts the graph downward

• Shifts the graph upward

What effect does a coefficient of 7 have on the graph of G(x) = 7x^2?

• Makes the graph wider

• Makes the graph narrower

• Reflects the graph over the x-axis

• Shifts the graph to the left