y= -x^2-12x+28

Question

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

Answer 1

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

Answer 2

Thank you so much