1.2 Transformations of Quadratics

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How does a positive 'k' value in vertex form affect the graph of a quadratic function?

Back

A positive 'k' value shifts the graph of the function upward.

Front

How does a negative 'k' value in vertex form affect the graph of a quadratic function?

Back

A negative 'k' value shifts the graph of the function downward.

Front

What effect does moving a quadratic function 5 units to the left have on its equation?

Back

The equation changes from y = ax² to y = a(x + 5)².

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 'h' value in vertex form represent?

Back

The 'h' value represents the x-coordinate of the vertex and indicates horizontal shifts.

Front

What is a vertical compression in the context of quadratic functions?

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider.

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the 'a' value is greater than 1, making the parabola narrower.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.