Transformations Of Quadratics

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 and a ≠ 0.

Front

What does it mean to reflect a graph in the x-axis?

Back

Reflecting a graph in the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

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. For example, f(x) = x² + k shifts the graph up if k > 0 and down if k < 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upward or downward.

Front

What does it mean to shift a graph horizontally?

Back

Shifting a graph horizontally involves moving it left or right. For example, f(x) = (x - h)² shifts the graph h units to the right.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

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

How do you determine if a quadratic function opens upward or downward?

Back

A quadratic function opens upward if the coefficient 'a' is positive (a > 0) and downward if 'a' is negative (a < 0).

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 equation x = -b/(2a).