Algebra test Please help ASAP

Question

3. A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

-Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

-Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

-Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add  to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

-What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

-Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

-In this problem, only positive values of x make sense. Why? (1 point)

-What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

-The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

Answer 1

1. The area of a rectangle is the product of its dimensions so the total area is y = (x+25)(x+9)
2. Using FOIL we get y = x² + 9x + 25x + (25)(9) = x² + 34x + 225
3. we can complete the square with y = (x+17)² - 17² + 225 = (x+17)² - 64 (note that I added and subtracted 17² in order to complete the square without changing its value)
4. Using the completed square formula, the vertex of the parabola is x = -17. On the other hand, the x-intercepts are where y = 0, which gives x = -9, -25. Finally the y-intercepts is where x = 0 which gives y = 225.
5. You can use desmos to graph this problem
6. this is when x = 0, i.e., the y-intercept
7. when x=6, y = 465

Hopefully, this answers your questions. Please let me know if you'd like anymore help!