Horizontal and Vertical Translations: Quadratic Functions

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2.

Front

What does a positive value inside the parentheses of a quadratic function indicate?

Back

A positive value inside the parentheses indicates a horizontal translation to the left.

Front

What does a negative value inside the parentheses of a quadratic function indicate?

Back

A negative value inside the parentheses indicates a horizontal translation to the right.

Front

What does a positive value outside the parentheses of a quadratic function indicate?

Back

A positive value outside the parentheses indicates a vertical translation upwards.

Front

What does a negative value outside the parentheses of a quadratic function indicate?

Back

A negative value outside the parentheses indicates a vertical translation downwards.

Front

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

Back

The vertex of a quadratic function in vertex form f(x) = a(x-h)^2 + k is (h, k).

Front

What transformation occurs in the function f(x) = (x - 3)^2 + 4?

Back

The graph is translated right 3 units and up 4 units.

Front

What transformation occurs in the function f(x) = (x + 1)^2 - 2?

Back

The graph is translated left 1 unit and down 2 units.

Front

How does the graph of f(x) = x^2 compare to g(x) = (x + 4)^2 + 1?

Back

The graph of g(x) is translated left 4 units and up 1 unit compared to f(x).

Front

What is the effect of changing the coefficient 'a' in the quadratic function f(x) = a(x - h)^2 + k?

Back

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