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The water height of a pool is determined by

8g^2 + 3g − 4, the rate that the pool is filled, and 9g^2 − 2g − 5, the rate that water leaves the pool, where g represents the number of gallons entering

or leaving the pool per minute.

AWrite an expression that determines the height of the water in the pool.
BWhat will be the height of the water if g = 1, 2, 3, and 4?
CTo the nearest tenth, at which value for g will the water reach its

greatest height? Explain.

Verified Answer :

Edufirst
AWater height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1

b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5

g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7

g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5

c) Greatest height

Find the vertex of the parabole

The vertex is at the mid point between the two roots.

To find the roots you can use the quadratic equation

The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2

The middle poin is 5/2 = 2.5

Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3


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