Quadratic Transformations Review

Front

What is the parent function of a quadratic function?

Back

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

Front

What effect does a coefficient greater than 1 have on the graph of a quadratic function?

Back

A coefficient greater than 1 causes a vertical stretch of the graph.

Front

What effect does a coefficient between 0 and 1 have on the graph of a quadratic function?

Back

A coefficient between 0 and 1 causes a vertical shrink of the graph.

Front

How does the equation y = (x - h)² + k transform the parent function y = x²?

Back

The equation translates the graph horizontally by h units and vertically by k units.

Front

What does the term 'vertical stretch' mean in the context of quadratic functions?

Back

Vertical stretch means that the graph is pulled away from the x-axis, making it narrower.

Front

What does the term 'vertical shrink' mean in the context of quadratic functions?

Back

Vertical shrink means that the graph is pushed towards the x-axis, making it wider.

Front

If the equation of a parabola is y = a(x - h)² + k, what do the parameters a, h, and k represent?

Back

a represents vertical stretch/shrink, h represents horizontal translation, and k represents vertical translation.

Front

What transformation does the equation y = x² - 3 represent?

Back

This equation represents a vertical translation down by 3 units.

Front

What transformation does the equation y = (x + 2)² + 1 represent?

Back

This equation represents a horizontal translation left by 2 units and a vertical translation up by 1 unit.

Front

How does the graph of y = (1/3)x² compare to the graph of y = x²?

Back

The graph of y = (1/3)x² is wider than the graph of y = x² due to the vertical shrink.