Transformation of Graphs M6L1

Front

What is a vertical translation of a graph?

Back

A vertical translation moves the graph up or down without changing its shape. For example, if a graph is translated 4 units up, every point on the graph moves up by 4 units.

Front

What is a horizontal translation of a graph?

Back

A horizontal translation shifts the graph left or right. For example, translating a graph 4 units left means every point on the graph moves left by 4 units.

Front

What does it mean for a graph to be stretched vertically?

Back

A vertical stretch occurs when the graph is pulled away from the x-axis, making it steeper. For example, a vertical stretch by a factor of 2 means that every y-coordinate is multiplied by 2.

Front

What is the effect of adding a constant to a function's output?

Back

Adding a constant to a function's output results in a vertical translation. For example, f(x) + 7 translates the graph of f up by 7 units.

Front

What is the effect of adding a constant to a function's input?

Back

Adding a constant to a function's input results in a horizontal translation. For example, f(x + 4) translates the graph of f left by 4 units.

Front

How do you identify a vertical translation in a function's equation?

Back

Look for a constant added or subtracted from the function. For example, in y = f(x) + 3, the graph is translated up 3 units.

Front

How do you identify a horizontal translation in a function's equation?

Back

Look for a constant added or subtracted inside the function's argument. For example, in y = f(x - 2), the graph is translated right 2 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

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

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.