Question

extended response

1. a. simplify the expression \\(\sqrt{25x + 150} - 2\\).

b. use the result from part (a) to graph the function \\(g(x) = \sqrt{25x + 150} - 2\\) and its parent function \\(f(x) = \sqrt{x}\\) in the same coordinate plane.

c. describe the graph of the function in relation to the graph of its parent function.

(graph: a coordinate plane with x-axis from -6 to 6 and y-axis from -6 to 6, grid lines present.)

Explanation:

Part a Step1: Factor inside square root

$\sqrt{25(x + 6)} - 2$

Part a Step2: Simplify square root

$5\sqrt{x + 6} - 2$

Part c Explanation:

• Horizontal shift: $x \to x+6$ means left 6 units.
• Vertical stretch: Coefficient 5 stretches by factor 5.
• Vertical shift: Subtract 2 means down 2 units.

Answer:

a. $5\sqrt{x + 6} - 2$
b. (Graph: Parent function $f(x)=\sqrt{x}$ starts at (0,0) and curves upward; $g(x)=5\sqrt{x+6}-2$ starts at (-6,-2), stretched vertically by 5)
c. Horizontal shift left 6, vertical stretch by 5, vertical shift down 2