4.2 Transformations of Quadratic Functions

Front

What transformation occurs when f(x) = x^2 is replaced with -f(x)?

Back

Reflection across the x-axis.

Front

What is the vertex of the function f(x) = 2(x - 5)^2 + 12?

Back

(5, 12)

Front

If f(x) = x^2, what is g(x) if g(x) is a vertical translation down by 5 units?

Back

g(x) = x^2 - 5

Front

What does it mean for a quadratic function to be 'stretched' or 'compressed'?

Back

A 'stretched' function has a larger leading coefficient, making it narrower, while a 'compressed' function has a smaller leading coefficient, making it wider.

Front

What is the effect of adding a constant to a quadratic function, such as f(x) = x^2 + 3?

Back

It results in a vertical translation upwards by 3 units.

Front

How does the graph of f(x) = (x - 2)^2 compare to f(x) = x^2?

Back

It is translated 2 units to the right.

Front

What transformation occurs when the function f(x) = x^2 is replaced with f(x) = x^2 + 4?

Back

Vertical translation up by 4 units.

Front

What is the effect of a negative leading coefficient in a quadratic function, such as f(x) = -x^2?

Back

It reflects the graph across the x-axis.

Front

If the graph of g(x) = -x^2 is transformed to create h(x), which is g(x) shifted up by 3 units, what is h(x)?

Back

h(x) = -x^2 + 3.

Front

What does the vertex of a quadratic function represent?

Back

The vertex represents the maximum or minimum point of the parabola.