Quadratic models! will mark i understand the concept of how to set them up, generally, but these are not turning out right 1. find a quadratic model for the annual amount in millions of dollars spent on water gardening based on number of years since 1999. round each coefficient to the nearest tenth. 2. the pizza prices for deangelo’s pizza parlor are shown below. find a quadratic model for the price of a pizza based upon the size (diameter).

There seems to be a strange typo in problem 1, but I'm not sure. So I'll skip it and move onto problem 2

The answer to problem 2 is y = -0.125x^2 + 5.25x - 35.05

Explanation:

We have the following points:

(12, 9.95) and (14, 13.95) and (16,16.95)

where x is the diameter in inches, y is the price in dollars

Use these three points to find the equation in the form y = ax^2 + bx + c

Plug in (x,y) = (12,9.95). Isolate c

y = ax^2 + bx + c

9.95 = a(12)^2 + b(12) + c

9.95 = 144a + 12b + c

9.95-144a-12b = c

c = 9.95-144a-12b

Plug in (x,y) = (14, 13.95)

Also, plug in c = 9.95-144a-12b

y = ax^2 + bx + c

13.95 = a(14)^2 + b(14) + c

13.95 = 196a + 14b + c

13.95 = 196a + 14b + 9.95-144a-12b

13.95 = 52a + 2b + 9.95

Solve for b

13.95 = 52a + 2b + 9.95

13.95-9.95 = 52a + 2b

4 = 52a + 2b

2b = -52a + 4

b = (-52a + 4)/2

b = -26a + 2

Plug in (x,y) = (16,16.95)

y = ax^2 + bx + c

16.95 = a(16)^2 + b(16) + c

16.95 = 256a + 16b + c

Now plug in c = 9.95-144a-12b

16.95 = 256a + 16b + c

16.95 = 256a + 16b + 9.95-144a-12b

16.95 = 112a + 4b + 9.95

16.95-9.95 = 112a + 4b

7 = 112a + 4b

112a + 4b = 7

Next, plug in b = -26a+2, and solve for 'a'

112a + 4b = 7

112a + 4(-26a+2) = 7

112a + 4(-26a)+4(2) = 7

112a - 104a + 8 = 7

8a + 8 = 7

8a = 7-8

8a = -1

a = -1/8

a = -0.125

Use that 'a' value to find b

b = -26a + 2

b = -26(-0.125) + 2

b = 5.25

Finally, use those 'a' and 'b' values to determine c

c = 9.95-144a-12b

c = 9.95-144(-0.125)-12(5.25)

c = -35.05

We found that

a = -0.125, b = 5.25, and c = -35.05

So y = ax^2 + bx + c turns into y = -0.125x^2 + 5.25x - 35.05

As a way to check the answer, we plug in the various x values to get the corresponding y values. For example, if x = 12, then

y = -0.125x^2 + 5.25x - 35.05

y = -0.125(12)^2 + 5.25(12) - 35.05

y = 9.95

Which is the proper y value we want. I'll let you check the others

y = 0.77(x)

step-by-step explanation:

the jacket retains this value after 23% cut or retains 77% of original value. plug original 87 jacket price for x and the remaining value should be y.

huh? im pretty sure it is in 199

step-by-step explanation: