Transformations of Quadratic 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

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 up or down.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What does a vertical shift in a quadratic function indicate?

Back

A vertical shift moves the graph up or down. For example, in f(x) = x² + k, k indicates the vertical shift: up if k > 0, down if k < 0.

Front

What does a horizontal shift in a quadratic function indicate?

Back

A horizontal shift moves the graph left or right. In f(x) = (x - h)², h indicates the horizontal shift: right if h > 0, left if h < 0.

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the 'a' value is greater than 1, making the parabola narrower. For example, f(x) = 2x² is a vertical stretch of f(x) = x².

Front

What is a vertical compression in a quadratic function?

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider. For example, f(x) = 0.5x² is a vertical compression of f(x) = x².

Front

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

Back

Reflection over the x-axis occurs when the 'a' value is negative, flipping the parabola upside down.

Front

How do you identify the direction a parabola opens?

Back

The direction a parabola opens can be identified by the sign of 'a': if 'a' > 0, it opens up; if 'a' < 0, it opens down.