8. A bakery is collecting data to investigate how changing the price charged for a loaf of bread
affects the bakery's daily profit. The graph shows the data the bakery has collected.
Bread Price vs. Daily Profit
1000
800
600
.
Daily Profit (Dollars)
.
.
400
.
.
200
0
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Price for One Loaf of Bread (Dollars)
Which quadratic function is the BEST model for the data?
A
8(1-4) - 800
В.
86
4) - 800
С
20001 - 1) --- 800
D
3000
4)- 800

A function is a mathematical expression that describes how factors are related. In this case, how the price is related to the profit.

How to determine if a function models the data?

The best way to determine this is to solve the expression and verify if the answer is correct.

For example, we know that at 4 (x) dollars, the daily profit is $800 (y). Let's now the different options:

A.

y= -8 (x+4)^2 + 800
y= -8 (4+4)^2 + 800
y= -8 (8)^2 + 800
y= -8 (36) + 800
y=-8 (288) + 800
y= -2304 + 800
y= -1504

B.

y= -8 (x-4)^2 + 800
y= -8 (4-4)^2 + 800
y= -8 (0)^2 + 800
y= -8 (0) + 800
y= 0 + 800
y= 800

C.

y= -200 (4+4)^2+ 800
y= -200 (8)^2 + 800
y= -200 (36) + 800
y= -200 (36) + 800
y= -7200 + 800
y= -6400

D.

y= -200 (x-4)^2 + 800
y= -200 (4-4)^2 + 800
y= -200 (0)^2 + 800
y= -200 (0) + 800
y= 0 + 800
y= 800

This means B and D are possible options, however, when verified with other results such as $6 the correct one is option D.

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raphealnwobi raphealnwobi · Answer 2 · 2022-03-15T12:39:30+01:00

The quadratic equation is given by y = -200x² + 1600x - 2400.

Quadratic equation formula

The standard form of the quadratic equation is:

y = ax² + bx + c

Where a,b,c are constants.

Let y represent the daily profit for x bread price.

At point (2, 0):

0 = a(2)² + b(2) + c

4a + 2b + c = 0 (1)

At point (4, 800):

800 = a(4)² + b(4) + c

16a + 4b + c = 800 (2)

At point (6, 0):

0 = a(6)² + b(6) + c

36a + 6b + c = 0 (3)

From all the equations:

a = -200, b = 1600, c = -2400

The quadratic equation is given by y = -200x² + 1600x - 2400.

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