Quadratic Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function affect?

Back

The 'a' value affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. Larger absolute values of 'a' make the parabola narrower.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

How does changing 'c' in y = ax² + bx + c affect the graph?

Back

Changing 'c' results in a vertical shift of the graph. Increasing 'c' shifts the graph up, while decreasing 'c' shifts it down.

Front

What transformation occurs when the equation is y = x² + 4?

Back

The graph of y = x² is shifted up 4 units.

Front

What transformation occurs when the equation is y = x² - 3?

Back

The graph of y = x² is shifted down 3 units.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y). This changes the sign of the output values.

Front

What happens to the graph of y = x² when it is transformed to y = -x²?

Back

The graph is reflected over the x-axis.

Front

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

Back

The graph of y = 1/3x² is wider than the graph of y = x².

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the 'a' value in y = ax² is greater than 1, making the parabola narrower.