Graphing a quadratic equation with a vertical stretch and shift

The video tutorial explains the vertex form of a quadratic function and its transformations, including horizontal compression and vertical shift. It demonstrates graphing the parent function y = X^2, identifying the vertex and axis of symmetry, and applying transformations to graph a new function. The tutorial emphasizes understanding transformations and using a table of values for accurate graphing.

What is the effect on the graph of a quadratic function when the absolute value of 'a' is greater than zero?

• Horizontal compression

• Vertical stretch

• Vertical shift

• Horizontal translation

What is the vertex of the parent graph y = x^2?

• (0, 0)

• (1, 1)

• (0, 1)

• (1, 0)

In the context of graph transformations, what does the 'H' in the vertex form y = (x - H)^2 + K represent?

• Vertical shift

• Horizontal translation

• Horizontal compression

• Vertical stretch

If a quadratic function is vertically shifted up by 4 units, what is the value of 'K' in the vertex form?

• -4

• 4

• 0

• 2

How does a horizontal compression by a factor of 2 affect the graph of a quadratic function?

• It shifts the graph to the right.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph upwards.

What is the new vertex of the graph after a vertical shift up by 2 units from the origin?

• (2, 0)

• (2, 2)

• (0, 2)

• (0, 0)

When graphing a transformed quadratic function, why is it useful to find two points to the right of the vertex?

• To determine the axis of symmetry

• To calculate the slope

• To reflect them over the axis of symmetry

• To find the y-intercept