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 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How does the 'h' value in the vertex form of a quadratic function y = a(x-h)² + k affect the graph?

Back

The 'h' value shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the 'k' value in the vertex form of a quadratic function affect?

Back

The 'k' value shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value reflects the graph across the x-axis.

Front

What does it mean to compress a quadratic function?

Back

To compress a quadratic function means to make the parabola narrower, which occurs when the absolute value of 'a' is greater than 1.

Front

What does it mean to stretch a quadratic function?

Back

To stretch a quadratic function means to make the parabola wider, which occurs when the absolute value of 'a' is less than 1.

Front

How do you identify the direction of a parabola?

Back

The direction of a parabola can be identified by the sign of 'a': positive means it opens upwards, and negative means it opens downwards.

Front

What transformation occurs when you add a constant to a quadratic function?

Back

Adding a constant shifts the graph vertically. For example, y = x² + 3 shifts the graph up 3 units.