Find the x-intercepts for the quadratic function y= -1/2(x+3)^2 +4

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284

gregory's graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2