Identify Transformations in Quadratic Functions

Front

What is a vertical compression in a quadratic function?

Back

A vertical compression occurs when the graph of a quadratic function is squeezed towards the x-axis, making it wider. This happens when the leading coefficient (a) is between 0 and 1.

Front

What does it mean to shift a quadratic function 5 units up?

Back

Shifting a quadratic function 5 units up means adding 5 to the entire function, resulting in a new vertex that is 5 units higher on the y-axis.

Front

What is a reflection across the x-axis in a quadratic function?

Back

A reflection across the x-axis occurs when the graph of the quadratic function is flipped over the x-axis, which happens when the leading coefficient (a) is negative.

Front

What does it mean to shift a quadratic function 4 units down?

Back

Shifting a quadratic function 4 units down means subtracting 4 from the entire function, resulting in a new vertex that is 4 units lower on the y-axis.

Front

What does it mean to shift a quadratic function 3 units right?

Back

Shifting a quadratic function 3 units right means replacing x with (x - 3) in the function, moving the graph 3 units to the right on the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/2a.

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the graph of a quadratic function is pulled away from the x-axis, making it narrower. This happens when the leading coefficient (a) is greater than 1.

Front

What is the effect of a horizontal stretch on a quadratic function?

Back

A horizontal stretch occurs when the graph of a quadratic function is widened. This happens when the x variable is multiplied by a factor less than 1.