Quadratic Transformations Mixed

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 f(x) = a(x - h)² + k represent?

Back

The 'a' value represents the vertical stretch or compression of the parabola. If |a| > 1, the graph is stretched; if 0 < |a| < 1, it is compressed.

Front

How does changing the 'h' value in the vertex form affect the graph?

Back

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

Front

How does changing the 'k' value in the vertex form affect the graph?

Back

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

Front

What transformation occurs when the quadratic function is written as f(x) = 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 is the effect of a negative 'a' value in the vertex form?

Back

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

Front

What does it mean for a quadratic function to be 'narrower'?

Back

A quadratic function is narrower when the absolute value of 'a' is greater than 1, indicating a steeper graph.

Front

What does it mean for a quadratic function to be 'wider'?

Back

A quadratic function is wider when the absolute value of 'a' is less than 1, indicating a flatter graph.

Front

Describe the transformation of the function f(x) = (x + 3)² - 2.

Back

The graph is shifted 3 units left and 2 units down.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.