4 - Solving Radicals and Graphing Features

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root or cube root. For example, @@ ext{radical} ext{ of } x = ext{ } oot{n}{x}@@.

Front

How do you solve an equation involving square roots?

Back

To solve an equation with square roots, isolate the radical on one side, square both sides to eliminate the radical, and then solve the resulting equation.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you identify extraneous solutions?

Back

To identify extraneous solutions, substitute the solutions back into the original equation to check if they hold true.

Front

What is the square root property?

Back

Front

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

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the effect of adding a constant to a square root function?

Back

Adding a constant to a square root function shifts the graph vertically. For example, @@y = ext{ } oot{2}{x} + c@@ shifts the graph up by c units.

Front

What is the domain of a square root function?

Back

The domain of a square root function is the set of all x-values for which the expression under the square root is non-negative.

Front

How do you graph a square root function?

Back

To graph a square root function, identify the vertex, determine the domain, and plot points by substituting x-values into the function.

Front

What is the transformation of the function @@y = ext{ } oot{2}{x} - 3@@?

Back

The transformation of the function @@y = ext{ } oot{2}{x} - 3@@ is a vertical shift down by 3 units.