2.6 Flashcard Piecewise Functions & Vertex Form

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The absolute value of 'a' affects the width of the parabola.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is determined by the individual domains of each piece and the conditions under which they apply.

Front

What does it mean for a graph to be shifted left or right?

Back

Shifting a graph left or right involves adding or subtracting a value from the x-variable in the function's equation.

Front

What does it mean for a graph to be stretched or shrunk?

Back

Stretching a graph means increasing the value of 'a' in the vertex form, making it narrower; shrinking means decreasing 'a', making it wider.

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

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

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting back to find y.