PHHSTransformations of Quadratic Functions

Front

What is a transformation of a quadratic function?

Back

A transformation of a quadratic function involves changing its position, shape, or orientation on the graph, which can include translations, reflections, stretches, and compressions.

Front

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

Back

Reflecting a quadratic function over the x-axis means that all the y-values of the function are multiplied by -1, resulting in a graph that is flipped upside down.

Front

How does the coefficient of a quadratic function affect its width?

Back

If the coefficient (a) is greater than 1, the graph is narrower; if it is between 0 and 1, the graph is wider. If a is negative, it also reflects the graph over the x-axis.

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's equation.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic function. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does a vertical shift of a quadratic function entail?

Back

A vertical shift involves adding or subtracting a constant from the function's output, moving the graph up or down.

Front

What is the effect of a horizontal shift on a quadratic function?

Back

A horizontal shift involves adding or subtracting a constant from the input variable x, moving the graph left or right.

Front

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

Back

The vertex of a quadratic function in standard form f(x) = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.