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# Quadratics, Definitions of Functions, Relationships Between Exponents & Logarithms, Inverse Functions.

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Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone?

Is the compound interest formula (such as would be used to calculate a car loan) an example of a function? If yes, of what type of function is it an example? Why might you identify it with that type of function?

What is the relationship between exponents and logarithms? How would you distinguish between the two, using both a graph and a sequence?

Find the inverse function: f(x) = 3 x^2 - 5

#### Solution Preview

Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone?

The length of a rectangle is N inches more than it's width. The area of the rectangle is C square inches. Find the dimensions of the rectangle.

steps:

1. We need equations that describe the situation.
2. We use the word problem and convert it to algebraic formulas:

"length of a rectangle is N inches more than it's width"

we denote L as length, W as width, then we have:

L = N+W

This is one equation. Another one is obtained from:
"area of the rectangle is C square inches"

The area (A) is length times width and it equals C.

A = L*W = (N+W)*W = C

If we expand:

W^2 + N*W = C
or
W^2 + N*W - C =0

Let's say now that we are given actual values for N and C. For example:
N = 3
C = 10