Write the equation of the axis of symmetty, and find the coordinates of the vertex of the graph of y=-x2-4x+5

The axis of symmetry is x = -2 and the vertex is (-2, 9)

Step-by-step explanation:

To find the vertex of the standard form equation, use the formula x = -b/2a. Then substitute -b/2a into the equation and solve for y.

Here a = -1, b = -4 and c = 5.

Substitute the values and solve.

x = -(-4)/2(-1)

x = 4/-2

x = -2

Substitute x = -2.

y = -(-2)^2 -4(-2) + 5

y = -4 + 8 + 5

y = 9

So the axis of symmetry is x = -2 and the vertex is (-2, 9).

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