How do you put word problems into quadratic equations and functions?

Question

Give me an example.

Answer 1

A number added to my square is equal to 90. What number is this?

Mentally, one might go, "Oh, that's easy; it's 9! Because 9 + 81 = 90!" However, is that really the case? We should determine this algebraically, as mathematics isn't about arbitrarily guessing.

Let x be the number in question. Then, translating the question,

x^2 + x = 90

Moving the 90 to the left hand side,

x^2 + x - 90 = 0

Factoring,

(x + 10) (x - 9) = 0

And now, we equate each of those to 0.

x + 10 = 0
x - 9 = 0

Which leads to the solution set x = {-10, 9}

As you can see, -10 also satisfies the word problem in addition to 9.

Answer 2

Ann has 2 apples and Mary 4 apples . Make a function to associate to each person her number of apples.

The velocity of a car has the equation:
a(t) = t^2-5t+4, where t is the time. Find when the velocity is 0.
Note: the velocity can be negative too unlike speed which is always postive.

Answer 3

It's really hard. Usually the function is given and the word problem is asking you to find the vertex or starting point.