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Andru [333]
3 years ago
8

Help!! Quadratic models! Will mark brainiliest!!

Mathematics
1 answer:
denis23 [38]3 years ago
7 0

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


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