Transformations of Parabolas

Front

What happens to the parabola when you multiply its equation by a number bigger than 1? (e.g., y = 3x²)

Back

The graph gets NARROWER.

Front

What transformation occurred to y = x² to y = (x - 5)² - 3?

Back

The graph translated right 5 units and down 3 units.

Front

When you add a constant to y = x² (e.g., y = x² + 2), what happens to the graph?

Back

The graph moves UP.

Front

Which way does the graph move if the equation looks like y = (x - 3)²?

Back

The graph moves to the RIGHT 3 units.

Front

In vertex form, y = a(x - h)² + k, what effect does the 'a' have on the graph?

Back

'a' dilates (stretches) the graph.

Front

What is the vertex of the parabola in the equation y = (x + 2)² - 4?

Back

The vertex is (-2, -4).

Front

How does the graph of y = -x² differ from y = x²?

Back

The graph opens DOWN instead of UP.

Front

What does the 'h' represent in the vertex form y = a(x - h)² + k?

Back

The 'h' represents the horizontal translation of the graph.

Front

What is the effect of subtracting a number from 'k' in the vertex form y = a(x - h)² + k?

Back

It translates the graph DOWN by that number.

Front

If the equation of a parabola is y = 2(x - 1)² + 3, what is the direction of opening?

Back

The parabola opens UP because 'a' is positive.