Transforming quadratics

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How does a translation of a function affect its graph?

Back

A translation shifts the graph of a function horizontally or vertically without changing its shape.

Front

What does a positive 'a' value in a quadratic function indicate about the graph's direction?

Back

A positive 'a' value indicates that the graph opens upwards.

Front

What does a negative 'a' value in a quadratic function indicate about the graph's direction?

Back

A negative 'a' value indicates that the graph opens downwards.

Front

How do you determine the vertex of a quadratic function in vertex form?

Back

In vertex form, f(x) = a(x - h)² + k, the vertex is the point (h, k).

Front

What effect does a vertical stretch have on the graph of a quadratic function?

Back

A vertical stretch by a factor of 'k' (where k > 1) makes the graph narrower.

Front

What is the effect of translating a quadratic function 3 units to the left?

Back

Translating a quadratic function 3 units to the left involves replacing x with (x + 3) in the function.

Front

How do you reflect a quadratic function over the x-axis?

Back

To reflect a quadratic function over the x-axis, multiply the entire function by -1.

Front

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

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction it opens.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form f(x) = ax² + bx + c.