Question

Linda is opening a bakery and needs to figure out how much to charge for donuts. She checks with a number of other bakeries and compares their prices to their reported profits.

Donut Price Profits
$1.55 $5244
$0.95 $5244
$0.75 $3900
$1.25. $6000
$1.05 $5664
$1.35. $5916
Bakery
Dan's Delicious Donuts
The Corner Bakery
Bake 'n Wake
Donuts 'R' Us
Dan's Delicious Donuts
Dan's Delicious Donuts $1.35

A: Find the quadratic function that fits this data. Express this function in vertex form.

B: Use your model to predict Linda's profits if she undercuts the competition by selling her donuts for 55 cents each.
Linda's profits will be $

Answer 1

A: To find the quadratic function that fits the given data, we can use the vertex form of a quadratic function: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Using the data provided, we can identify three points that lie on the parabola: (0.95, 5244), (1.35, 5916), and (1.55, 5244). Substituting these values into the vertex form, we can solve for a, h, and k.

Using the point (h, k) = (1.35, 5916), we have:

5916 = a(1.35 - h)^2 + k

Substituting (1.35, 5916) and (0.95, 5244) into the equation, we get:

5916 = a(1.35 - h)^2 + k
5244 = a(0.95 - h)^2 + k

Solving these two equations simultaneously will give us the values of a, h, and k. After obtaining the values, we can express the quadratic function in vertex form.

B: To predict Linda's profits if she sells her donuts for 55 cents each, we would need to substitute x = 0.55 into the quadratic function and solve for y. However, without the quadratic function in vertex form, we cannot provide an accurate prediction at this moment.