Quadratic Transformations_Period 2&4

Front

What is a quadratic function?

Back

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

Front

What does it mean to vertically stretch a quadratic function?

Back

Vertically stretching a quadratic function means multiplying the function by a factor greater than 1, which makes the graph narrower.

Front

What does it mean to vertically compress a quadratic function?

Back

Vertically compressing a quadratic function means multiplying the function by a factor between 0 and 1, which makes the graph wider.

Front

How does shifting a graph up affect its equation?

Back

Shifting a graph up by k units adds k to the function, changing f(x) to f(x) + k.

Front

How does shifting a graph down affect its equation?

Back

Shifting a graph down by k units subtracts k from the function, changing f(x) to f(x) - k.

Front

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

Back

The vertex of a quadratic function in vertex form, y = a(x - h)² + k, is the point (h, k).

Front

What does a negative 'a' value indicate in a quadratic function?

Back

A negative 'a' value indicates that the parabola opens downward.

Front

What is the effect of a positive 'a' value greater than 1 on the graph of a quadratic function?

Back

A positive 'a' value greater than 1 vertically stretches the graph, making it narrower.

Front

What is the effect of a positive 'a' value between 0 and 1 on the graph of a quadratic function?

Back

A positive 'a' value between 0 and 1 vertically compresses the graph, making it wider.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form, y = ax² + bx + c, is given by the formula x = -b/(2a).