Quadratic transformations

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

What transformation occurs when the equation is y = (x - h)²?

Back

The graph shifts horizontally to the right by h units if h is positive and to the left if h is negative.

Front

What transformation occurs when the equation is y = (x)² + k?

Back

The graph shifts vertically up by k units if k is positive and down if k is negative.

Front

What does a negative sign in front of a quadratic function indicate?

Back

It indicates a reflection over the x-axis.

Front

What is the axis of symmetry for the function f(x) = (x - 3)² + 2?

Back

The axis of symmetry is x = 3.

Front

How does the graph of y = x² compare to y = x² + 4?

Back

The graph of y = x² + 4 is the same shape as y = x² but shifted up 4 units.

Front

What effect does multiplying a quadratic function by a number greater than 1 have on its graph?

Back

It vertically stretches the graph.

Front

What effect does multiplying a quadratic function by a number between 0 and 1 have on its graph?

Back

It vertically compresses the graph.

Front

What is the vertex of the function f(x) = (x + 2)² - 3?

Back

The vertex is (-2, -3).

Front

What transformation occurs when the equation is y = - (x - 1)² + 5?

Back

The graph is reflected over the x-axis, shifted right 1 unit, and shifted up 5 units.