Posted by **nancy** on Sunday, March 31, 2013 at 8:30pm.

y= -x^2-12x+28

A painter can use the formula A=2/3bh to estimate the area of space under the parabola.

Calculate area in square ft under each arch

~ if there are 8 arches to be painted how many square ft must be painted

~ if 1 gallon paints 200 square ft , how many gallons must be needed

~ if a gallon of paint cost $27.00 and sales tax is 8% how much will it cost topaint 8 arches

- algebra -
**Reiny**, Sunday, March 31, 2013 at 9:33pm
y = -(x^2 + 12x - 28)

= -(x+14)(x-2)

So the parabola has x-intercepts at -14 and 2

so the vertex has an x-value of -6

(the midpoint between the intercepts)

sub in x=-6

y = -(8)(-8) = 64

so the base of the parabola is 16 and its height is 64

estimate of area = (2/3)(16)(64) = 682 2/3 square feet.

so 8 of those = 5461 1/3

number of gallons needed = 5461 1/3 ÷ 200 = 27.30666

we will need 28 gallons, can't buy .3066 of a gallon

cost = 1.08(28)(27) = $816.48

- algebra -
**nancy**, Sunday, March 31, 2013 at 11:20pm
Thank you so much

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