Quadratic Transformations Notes Quiz

What is the basic form of the quadratic parent function?

• f(x) = x

• f(x) = x^2

• f(x) = x^3

• f(x) = 1/x

What happens to the graph of the quadratic parent function f(x) = x^2 when it is transformed by f(x) + d?

• It shifts horizontally by d units.

• It stretches vertically by a factor of d.

• It shifts vertically by d units.

• It reflects over the x-axis.

If the quadratic function f(x) is transformed by f(x) - d, in which direction does the graph shift?

• Up by d units

• Down by d units

• Left by d units

• Right by d units

How does the transformation f(x - c) affect the graph of the quadratic parent function f(x) = x^2?

• It shifts the graph vertically by c units.

• It shifts the graph horizontally by c units.

• It stretches the graph horizontally by a factor of c.

• It reflects the graph over the y-axis.

When the quadratic function f(x) is transformed by f(x + c), in which direction does the graph shift?

• Up by c units

• Down by c units

• Left by c units

• Right by c units

When the quadratic function f(x) = x^2 is transformed by af(x), and |a| > 1, how is the graph affected?

• It undergoes a horizontal stretch

• It undergoes a vertical stretch

• It becomes wider

• It undergoes a horizontal compression

What happens to the graph of the quadratic function f(x) = x^2 when it is transformed by f(bx), and 0 < |b| < 1?

• It undergoes a vertical compression

• It becomes narrower

• It undergoes a horizontal stretch

• It undergoes a vertical stretch

If the quadratic function f(x) = x^2 is transformed by -f(x), which of the following statements is true?

• The graph flips across the y-axis

• The graph remains unchanged

• The graph flips across the x-axis

• The graph becomes wider

What is the effect on the graph of the quadratic function f(x) = x^2 when the transformation -f(x) is applied?

• The parabola will open upward

• The parabola will open to the right

• The parabola will open to the left

• The parabola will open downward

What transformation is applied to the function f(x) = x^2 to create the function g(x) = f(x) - 2.5?

• Horizontal shift to the right by 2.5 units

• Vertical stretch by a factor of 2.5

• Vertical shift down by 2.5 units

• Reflection across the y-axis