Alg. 2 Transformations of quadratic functions

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How do you translate a quadratic function to the right?

Back

To translate a quadratic function to the right, subtract a value from x in the function: f(x) = a(x - h)² + k, where h is the number of units to move right.

Front

How do you translate a quadratic function upward?

Back

To translate a quadratic function upward, add a value to k in the vertex form: f(x) = a(x - h)² + k, where k is the number of units to move up.

Front

What is the effect of reflecting a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis changes the sign of 'a' in the vertex form: f(x) = -a(x - h)² + k.

Front

What does it mean to stretch a quadratic function vertically?

Back

Stretching a quadratic function vertically means increasing the absolute value of 'a' in the vertex form, making the parabola narrower.

Front

What does it mean to compress a quadratic function vertically?

Back

Compressing a quadratic function vertically means decreasing the absolute value of 'a' in the vertex form, making the parabola wider.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in vertex form f(x) = a(x - h)² + k is x = h.

Front

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

Back

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

Front

How do you determine the direction a parabola opens?

Back

The direction a parabola opens is determined by the sign of 'a': if a > 0, it opens upward; if a < 0, it opens downward.