Exploring Quadratic Function Transformations

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 role of the vertex in these transformations.

What is the basic form of a quadratic function?

• f(x) = x^2

• f(x) = x^3

• f(x) = 2x

• f(x) = x

How does the graph of f(x) = x^2 + k shift when k is positive?

• Shifts down k units

• Shifts up k units

• Shifts left k units

• Shifts right k units

If k is negative in the function f(x) = x^2 + k, how does the graph shift?

• Shifts down k units

• Shifts right k units

• Shifts up k units

• Shifts left k units

In the function f(x) = (x - h)^2, what happens when h is positive?

• Shifts left h units

• Shifts right h units

• Shifts up h units

• Shifts down h units

How does the graph of f(x) = (x - h)^2 shift when h is negative?

• Shifts left h units

• Shifts right h units

• Shifts up h units

• Shifts down h units

What effect does a value of a > 1 have on the graph of f(x) = ax^2?

• Shifts the graph up

• Makes the graph narrower

• Reflects the graph across the x-axis

• Makes the graph wider

When 0 < a < 1 in the function f(x) = ax^2, what happens to the graph?

• The graph becomes wider

• The graph becomes narrower

• The graph shifts up

• The graph shifts down

What happens to the graph of f(x) = ax^2 when a is negative?

• The graph shifts up

• The graph shifts down

• The graph reflects across the x-axis

• The graph becomes wider

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

• (0, 0)

• (h, a)

• (h, k)

• (a, k)

How do you graph f(x) = 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