1.5 Transforming Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How does translating a function to the left affect its equation?

Back

To translate a function left by 'h' units, replace x with (x + h) in the function's equation.

Front

What does the vertex form of a quadratic function look like?

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 is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value reflects the parabola across the x-axis, making it open downwards.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of 'a' in the quadratic function: if 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

What does it mean to translate a function up or down?

Back

Translating a function up or down involves adding or subtracting a constant from the function's output (y-value). For example, f(x) + k translates the graph up by k units.

Front

What is the parent function of a quadratic?

Back

The parent function of a quadratic is f(x) = x², which is the simplest form of a quadratic function.

Front

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

Back

In vertex form f(x) = a(x - h)² + k, the vertex is the point (h, k).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How does a translation of a function affect its graph?

Back

A translation shifts the graph of the function without changing its shape. It can move the graph left, right, up, or down.