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 the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

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.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down without changing its shape. For example, f(x) = x² + k shifts the graph up if k > 0 and down if k < 0.

Front

What does it mean to shift a graph horizontally?

Back

Shifting a graph horizontally means moving it left or right. For example, f(x) = (x - h)² shifts the graph right if h > 0 and left if h < 0.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis occurs when the graph of a function f(x) is transformed to -f(x), flipping it over the x-axis.

Front

What does it mean for a parabola to be narrower or wider?

Back

A parabola is narrower if the absolute value of 'a' is greater than 1 (e.g., f(x) = 2x²), and wider if the absolute value of 'a' is less than 1 (e.g., f(x) = 0.5x²).

Front

How does the value of 'a' affect the direction of a parabola?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

Adding a constant shifts the graph vertically. For example, f(x) = x² + 3 shifts the graph up by 3 units.