Transformations of Quadratic Functions

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 stretch a quadratic function vertically?

Back

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

Front

What does it mean to compress a quadratic function vertically?

Back

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

Front

How does a positive 'a' value affect the graph of a quadratic function?

Back

A positive 'a' value opens the parabola upwards.

Front

How does a negative 'a' value affect the graph of a quadratic function?

Back

A negative 'a' value opens the parabola downwards.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of subtracting a constant from the x variable in a quadratic function?

Back

Subtracting a constant from the x variable shifts the graph horizontally. If you subtract a positive number, the graph shifts to the right; if you subtract a negative number, it shifts to the left.

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis means multiplying the entire function by -1, which flips the graph upside down.

Front

What is the vertex of 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

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.