Question

Y=(x-9)^(2)

(a) translation 9 units down
(b) y=x^(2)-9 B. a translation 9 units to the right
(c) y=9x^(2) C. a translation 9 units up
(d) y=(x+9)^(2) D. a translation 9 units to the left

Answer 1

The student's question pertains to algebraic transformations of the quadratic equation y = (x - 9)^2, where specific translations alter the graph vertically or horizontally.

Step-by-step explanation:

The student's question is about understanding how different algebraic manipulations translate to changes in the graph of a quadratic equation y = (x - 9)^2. Specifically, transformations such as translations are being analyzed here. Let's go through each alteration mentioned:

• (a) A translation 9 units down would modify the equation to y = (x - 9)^2 - 9.
• (b) A translation 9 units to the right would change the equation to y = (x - (9 + 9))^2 simplifying to y = (x - 18)^2.
• (c) A translation 9 units up would adjust the equation to y = (x - 9)^2 + 9.
• (d) A translation 9 units to the left results in the equation y = (x - (9 - 9))^2 which simplifies to y = x^2.

These transformations shift the graph of the original equation either vertically or horizontally.