How do you do solve 13 a and b?

Step-by-step explanation:

Let A=ax²+bx+c

x=1,A=a+b+c or 7=a+b+c   ...(1)

x=2,A=4a+2b+c or 12=4a+2b+c   ...(2)

x=3,A=9a+3b+c or 15=9a+3b+c   ...(3)

subtract (1) from (2) & (3)

3a+b=5   ...(4)

8=8a+2b

or 4a+b=4   ...(5)

subtract (4) from (5)

a=-1

from (4)

-3+b=5

b=5+3=8

b=8

from (1)

-1+8+c=7

c=0

so A=-x²+8x

thus  table shows it is quadratic.

b.

A=-x²+8x=-(x²-8x+16-16)

or A=-(x-4)²+16

vertex is (4,16)

1) 651.5 cm²

2) 462 cm²

3) 99 ft²

4) 1540.8 yd²

Step-by-step explanation:

1) Area of the trapezoid: (12 + 7)/2 * 6.5 = 61.75 cm²

Area of the lateral rectangles: 7*16 = 112 cm²

Area of the top rectangle: 12*16 = 192 cm²

Area of the bottom rectangle: 7*16 = 112 cm²

Area of the figure: 192 + 112 + 2*61.75 + 2*112 = 651.5 cm²

2) Area of the top and bottom squares: 11*11 = 121 cm²

Area of the lateral rectangles: 11*5 = 55 cm²

Area of the figure: 4*55 + 2*121 = 462 cm²

3)  Area of the trapezoid: (3 + 7)/2 * 3.5 = 17.5 ft²

Area of the lateral rectangles: 4*4 = 16 ft²

Area of the top rectangle: 7*4 = 28 ft²

Area of the bottom rectangle: 3*4 = 12 ft²

Area of the figure: 28 + 12 + 2*17.5 + 2*12 = 99 ft²

4) Area of the lateral rectangles: 11*12 = 132 yd²

Area of the top and bottom hexagons: 3*12*10.4 = 374.4 yd²

Area of the figure: 6*132 + 2*374.4 = 1540.8 yd²