vertical and horizontal shifts of quadratic functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the parent function of a quadratic function?

Back

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

Front

What does a horizontal shift of a quadratic function involve?

Back

A horizontal shift involves adding or subtracting a value inside the parentheses of the function, such as f(x) = (x - h)^2, where h is the shift.

Front

What does a vertical shift of a quadratic function involve?

Back

A vertical shift involves adding or subtracting a value outside the parentheses of the function, such as f(x) = x^2 + k, where k is the shift.

Front

How does the equation f(x) = (x + 3)^2 transform the parent function?

Back

It shifts the graph of the parent function 3 units to the left.

Front

How does the equation f(x) = x^2 - 5 transform the parent function?

Back

It shifts the graph of the parent function 5 units down.

Front

What is the vertex of the function f(x) = (x - 2)^2 + 3?

Back

The vertex is (2, 3).

Front

What is the effect of a negative sign in front of a quadratic function, such as f(x) = -x^2?

Back

It reflects the graph of the function across the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex.