Question

rewrite the function to make it easy to graph using transformations of its parent function. describe the graph.
y = \sqrt{25x - 50} - 3

y = \square (simplify your answer.)

Explanation:

Step1: Factor out the coefficient inside the square root

First, we factor out 25 from the expression inside the square root: \(25x - 50 = 25(x - 2)\). So the function becomes \(y=\sqrt{25(x - 2)}-3\).

Step2: Simplify the square root

We know that \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)). Here, \(a = 25\) and \(b=(x - 2)\), and \(\sqrt{25}=5\). So we can simplify \(\sqrt{25(x - 2)}\) to \(5\sqrt{x - 2}\). Thus, the function is rewritten as \(y = 5\sqrt{x - 2}-3\).

Answer:

\(y = 5\sqrt{x - 2}-3\)