Chayil H.

asked • 06/01/16

can you help me with my hw

John and Sarah are each saving money for a car. The total amount of money John will save is represented by the function       f(x) = 60 +5x. The total amount of money Sarah will save is given by the function g(x)=x^2 +46. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

1 Expert Answer


Richard C. answered • 06/01/16

5 (60)

Yes, You Can Learn Math!

Chayil H.

why do you need to factor?


Richard C.

Any quadratic function (the largest power of x is 2 like the one in your problem) has two solutions.  A quadratic, when graphed, looks like a parabola.  Sometimes, the parabola crosses the x-axis at two places: two solutions for x.
In the case here, we needed to factor the quadratic to find what the two x's are.  Any quadratic factored will look like:
(ax + c)(bx + c)
The two factors we found have this appearance.  The reason we only used one of them is because we needed to find weeks and that can't be negative.
Make sense?


Richard C.

meant (ax + c)(bx + d).


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