Question

John and Sarah are each saving money for a car. The total amount of money John will save is given by the function j(x)= x^2 +2x, where x represents the number of weeks. The total amount of money Sarah will save is given by the function s(x)= -3x+6, where x represents the numbers of weeks.

Explain the point of intersection in context to the problem. Show all work

Answer 1

See below.

Explanation:

Where the graphs of the functions intersect it represents the number of weeks when they have both saved the same amount of money. So by solving the system we can find the number of weeks and that amount of money.

y = x^2 + 2x

y = -3x + 6 so

x^2 + 2x = -3x + 6

x^2 + 5x - 6 = 0

(x + 6)(x - 1) = 0

So x = 1 ( we ignore the negative)

So after 1 week they have saved the same amount and the amount is -3 + 6 = 3.

Are you sure that -3x + 6 is right - because Sarah does not save anything after year 1 . The equation has a negative slope!!