Quadratic Transformations

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

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

Back

The value of 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What does a horizontal shift in a quadratic function mean?

Back

A horizontal shift occurs when the 'x' value in the vertex form is adjusted. For example, f(x) = a(x-h)² + k shifts the graph h units to the right if h is positive and to the left if h is negative.

Front

What does a vertical shift in a quadratic function mean?

Back

A vertical shift occurs when the 'k' value in the vertex form is adjusted. For example, f(x) = a(x-h)² + k shifts the graph k units up if k is positive and down if k is negative.

Front

What is the parent function of a quadratic equation?

Back

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

Front

How do you identify the vertex of the function f(x) = -2(x-1)² + 3?

Back

The vertex is (1, 3). This is derived from the vertex form f(x) = a(x-h)² + k, where (h,k) is the vertex.

Front

What transformations occur when changing from y = x² to y = 2(x+2)² - 5?

Back

The graph is stretched vertically by a factor of 2, shifted 2 units left, and 5 units down.

Front

What does it mean to reflect a quadratic function across the x-axis?

Back

Reflecting a quadratic function across the x-axis means multiplying the function by -1, which flips the graph upside down.

Front

How do you determine if a quadratic function is compressed or stretched?

Back

If the absolute value of 'a' in the vertex form f(x) = a(x-h)² + k is greater than 1, the graph is stretched. If it is between 0 and 1, the graph is compressed.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function results in a vertical shift of the graph. For example, f(x) = x² + 5 shifts the graph 5 units up.