algebra
posted by nancy on .
y= x^212x+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

y = (x^2 + 12x  28)
= (x+14)(x2)
So the parabola has xintercepts at 14 and 2
so the vertex has an xvalue 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 รท 200 = 27.30666
we will need 28 gallons, can't buy .3066 of a gallon
cost = 1.08(28)(27) = $816.48 
Thank you so much