Transformations of Quadratic Functions

Front

What is a vertical shift in a quadratic function?

Back

A vertical shift moves the graph of the function up or down without changing its shape. For example, f(x) = x^2 + k shifts the graph up if k > 0 and down if k < 0.

Front

What does a horizontal translation do to the graph of a quadratic function?

Back

A horizontal translation moves the graph left or right. For example, f(x) = (x - h)^2 shifts the graph right if h > 0 and left if h < 0.

Front

What is the effect of a negative coefficient in front of a quadratic function?

Back

A negative coefficient reflects the graph across the x-axis. For example, f(x) = -x^2 opens downward.

Front

How does vertical compression affect the graph of a quadratic function?

Back

Vertical compression reduces the steepness of the graph. For example, f(x) = (1/2)x^2 compresses the graph vertically by a factor of 1/2.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2, which is a parabola that opens upwards.

Front

What transformation occurs in the function g(x) = (x + 4)^2?

Back

This function represents a horizontal translation 4 units to the left from the parent function.

Front

What does the equation f(x) = 2x^2 + 3 represent?

Back

This equation represents a vertical stretch by a factor of 2 and a vertical shift up 3 units from the parent function.

Front

How do you identify a vertical shift in a quadratic function?

Back

A vertical shift can be identified by the constant added or subtracted from the function, such as in f(x) = x^2 + k.

Front

What is the transformation represented by g(x) = -1/5(x - 1)^2 + 7?

Back

This function includes a reflection across the x-axis, a vertical compression by a factor of 1/5, a horizontal shift right 1 unit, and a vertical shift up 7 units.

Front

What does the term 'reflection' mean in the context of quadratic functions?

Back

Reflection means flipping the graph over a specific axis. A negative coefficient reflects the graph over the x-axis.