6.1 Radical Equations

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, square both sides to eliminate the radical, and then solve for the variable.

Front

What is the parent function of a square root function?

Back

The parent function is f(x) = √x.

Front

What is the domain of the square root function f(x) = √x?

Back

The domain is [0, ∞).

Front

What is the range of the square root function f(x) = √x?

Back

The range is [0, ∞).

Front

How does the graph of y = √(x - 3) differ from y = √x?

Back

It shifts the graph of y = √x to the right by 3 units.

Front

What is the effect of adding a constant outside the radical, e.g., y = √x + 2?

Back

It shifts the graph vertically upwards by 2 units.

Front

What is the effect of subtracting a constant outside the radical, e.g., y = √x - 2?

Back

It shifts the graph vertically downwards by 2 units.

Front

What is the effect of adding a constant inside the radical, e.g., y = √(x + 3)?

Back

It shifts the graph to the left by 3 units.

Front

What is the effect of subtracting a constant inside the radical, e.g., y = √(x - 3)?

Back

It shifts the graph to the right by 3 units.