8.4 Transformations

Front

What is the vertex of the quadratic function f(x) = -x^2 - 4x + 12?

Back

The vertex is (-2, 16).

Front

If g(x) = f(x) + 3, what is the vertex of g(x) if the vertex of f(x) is (-2, 16)?

Back

The vertex of g(x) is (-2, 19).

Front

Which 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 g(x) = f(x + 2) if the vertex of f(x) is (-4, 5)?

Back

The vertex of g(x) is (-6, 5).

Front

What is the correct equation for the graph that has a vertex at (-2, -1)?

Back

f(x) = (x + 2)^2 - 1.

Front

If f(x) = -2x^2 + 4x + 3 has a vertex at (1, 5), what is the vertex of g(x) = f(x - 2)?

Back

The vertex of g(x) is (3, 5).

Front

What does a vertical translation of a function mean?

Back

It means shifting the graph up or down without changing its shape.

Front

What is the effect of a horizontal translation on the graph of a function?

Back

It shifts the graph left or right.

Front

How does the graph of f(x) = x^2 change when multiplied by a negative number?

Back

The graph reflects across the x-axis.

Front

What is the effect of adding a constant to a function, such as g(x) = f(x) + k?

Back

It translates the graph vertically by k units.