Graph Transformations of Quadratic Functions

This video tutorial covers transformations of quadratic functions, focusing on how changes in the parameters 'k', 'h', and 'a' affect the graph of the basic quadratic function f(x) = x^2. It explains vertical shifts with 'k', horizontal shifts with 'h', and vertical stretching or compression with 'a'. The tutorial also demonstrates how to combine these transformations to graph complex quadratic functions, emphasizing the importance of understanding each parameter's role in altering the graph's shape and position.

What is the basic form of a quadratic function?

• f(x) = x^3

• f(x) = x^2

• f(x) = x

• f(x) = 2x

How does the graph of y = x^2 + k change when k is positive?

• It shifts upward.

• It shifts to the left.

• It shifts to the right.

• It shifts downward.

What happens to the graph of y = x^2 + k when k is negative?

• It becomes wider.

• It shifts downward.

• It becomes narrower.

• It shifts upward.

In the equation y = (x - h)^2, what does a positive h do to the graph?

• Shifts it to the left.

• Shifts it to the right.

• Stretches it vertically.

• Compresses it vertically.

What effect does a negative h have in the equation y = (x - h)^2?

• Reflects the graph over the x-axis.

• Shifts the graph to the left.

• Shifts the graph to the right.

• Reflects the graph over the y-axis.

What happens to the graph of y = ax^2 when a > 1?

• It shifts upward.

• It becomes narrower.

• It becomes wider.

• It shifts downward.

How does the graph of y = ax^2 change when 0 < a < 1?

• It becomes narrower.

• It becomes wider.

• It shifts to the right.

• It shifts to the left.

What is the effect of a negative a in the equation y = ax^2?

• The graph reflects over the x-axis.

• The graph shifts downward.

• The graph shifts upward.

• The graph reflects over the y-axis.

In the equation y = a(x - h)^2 + k, what is the vertex of the parabola?

• (0, 0)

• (h, k)

• (a, k)

• (h, a)

How do you graph y = 2(x - 1)^2 + 3 using transformations?

• Shift right 1 unit, then up 3 units.

• Shift left 1 unit, then down 3 units.

• Shift left 1 unit, then up 3 units.

• Shift right 1 unit, then down 3 units.