apex algebra test 3.8.4

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.
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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. a. 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)
b. Rewrite the area equation in standard form. Hint: Use the FOIL method. (1
point)
c. 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)
d. 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)
(
2
b )
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3.8.4
Test (TST): Quadratic Equations and Functions 6/12
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e. Graph the parabola. Use the key features of the graph that you identified in Part
d. (3 points)
f. In this problem, only positive values of x make sense. Why? (1 point)
g. What point on your graph shows a total area that includes the pool but not the
pool deck? (1 point)
h. 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