The price of a stock, A(x), over a 12-month period decreased and then increased according to the question A(x)= 0.75x2-6x+20, where x equals the number of months. The price of another stock, B(x), increased according to the equation B(x)=2.75x+1.50 over the same 12-month period. Graph and label both equations on the accompanying grid. State all prices, to the nearest dollar, when both stock values were the same.

Question

The price of a stock, A(x), over a 12-month period decreased and then increased according to the question A(x)= 0.75x2-6x+20, where x equals the number of months. The price of another stock, B(x), increased according to the equation B(x)=2.75x+1.50 over the same 12-month period. Graph and label both equations on the accompanying grid. State all prices, to the nearest dollar, when both stock values were the same.

Answer 1

We cannot draw graphs for you here. That is an exercise you should do yourself.

The prices are the same when
0.75 x^2 -6x + 20 = 2.75 x + 150
which can be rewritten
0.75 x^2 -8.75 x -130 = 0

Solve for x using the quadratic equation and use the value(s) of x that you get to calculate the price. Ignore any negative x values

Answer 2

$9 and $26

I found this using graphs and intersections.

Answer 3

To find the prices when both stock values were the same, we need to solve the equations A(x) = B(x).

The given equations are:
A(x) = 0.75x^2 - 6x + 20
B(x) = 2.75x + 1.5

To graph these equations on a grid, we can plot several points and connect them with a curve. Let's choose some values for x and calculate the corresponding y-values using the equations.

Let's start with A(x):
For x = 0: A(0) = 0.75(0)^2 - 6(0) + 20 = 20
For x = 1: A(1) = 0.75(1)^2 - 6(1) + 20 = 14.75
For x = 2: A(2) = 0.75(2)^2 - 6(2) + 20 = 14
For x = 3: A(3) = 0.75(3)^2 - 6(3) + 20 = 15.75

Now let's calculate B(x):
For x = 0: B(0) = 2.75(0) + 1.5 = 1.5
For x = 1: B(1) = 2.75(1) + 1.5 = 4.25
For x = 2: B(2) = 2.75(2) + 1.5 = 7
For x = 3: B(3) = 2.75(3) + 1.5 = 9.25

Now we can plot these points on the grid and connect them to form the curves for A(x) and B(x).

Based on the graph, we can see that the curves intersect at some point, indicating when the prices of both stocks were the same.

To find the exact prices, we can solve the equation A(x) = B(x) algebraically.

0.75x^2 - 6x + 20 = 2.75x + 1.5

Simplifying the equation:
0.75x^2 - 9.75x + 18.5 = 0

To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

Substituting the values:
x = (9.75 ± √(9.75^2 - 4*0.75*18.5)) / (2*0.75)

Simplifying further will give us two values for x. By substituting these values back into either A(x) or B(x) equations, we can get the corresponding prices for both stocks when they were the same.