Transformations of Quadratics

Front

What transformation occurs in the equation y = (x - 5)² - 3?

Back

The graph is shifted to the right 5 units and down 3 units.

Front

In the vertex form y = a(x - h)² + k, what does the value of k represent?

Back

The value of k translates the graph vertically (up or down).

Front

What is the effect of changing the sign of a in the vertex form of a quadratic equation?

Back

It reflects the graph across the x-axis.

Front

What is the vertex of the quadratic equation y = (x - 3)² + 4?

Back

The vertex is at the point (3, 4).

Front

How does the graph of y = (x - 3)² differ from y = x²?

Back

The graph moves to the right 3 units.

Front

What does the term 'reflection' mean in the context of quadratic transformations?

Back

Reflection means flipping the graph over a specific axis, such as the x-axis.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

How does the value of a affect the width of the parabola in a quadratic function?

Back

If |a| > 1, the parabola is narrower; if |a| < 1, it is wider.

Front

What does the term 'vertical translation' refer to in quadratic transformations?

Back

Vertical translation refers to moving the graph up or down along the y-axis.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on the direction it opens.