Quadratic Transformations

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

What transformation occurs when a quadratic function is written in the form f(x) = a(x - h)² + k?

Back

The transformation includes a horizontal shift by h units and a vertical shift by k units.

Front

What does the 'a' value in the quadratic function f(x) = a(x - h)² + k indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the vertical stretch or compression (|a| > 1 stretches, 0 < |a| < 1 compresses).

Front

How does a negative 'a' value affect the graph of a quadratic function?

Back

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

Front

What does a vertical shift of k units mean in the context of a quadratic function?

Back

A vertical shift of k units means the entire graph moves up if k > 0 and down if k < 0.

Front

What is the effect of a horizontal shift of h units on the graph of a quadratic function?

Back

A horizontal shift of h units means the graph moves to the right if h > 0 and to the left if h < 0.

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 vertex from the standard form of a quadratic function?

Back

The vertex can be found using the formula (h, k) from the vertex form f(x) = a(x - h)² + k.

Front

What does it mean for a quadratic function to have a vertical shrink?

Back

A vertical shrink occurs when the absolute value of 'a' is less than 1, making the parabola wider.

Front

What transformations are represented by the equation g(x) = -1/5(x - 1)² + 7?

Back

The transformations are a reflection over the x-axis, a vertical shrink by a factor of 1/5, a right shift of 1 unit, and an upward shift of 7 units.