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# Algebra

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1) Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x)=-2x(squared) + 8X - 1

2) An equation of a quadratic function is given -- f(x)= -2X(squared) - 12X + 3
- Determine without graphing, whether the function has a minimum value or a maximum value.
- Find the minimum or maximum value and determine where it occurs.
- Identify the function's domain and it's range.

3) Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible, what is the maximum product?

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#### Solution Preview

We have the following facts about a quadratic function f(x)=ax^2+bx+c.
(1) If a>0, it has minimum point at x=-b/2a, the vertex is at (-b/2a, f(-b/2a)). The parabola is open upward.
(2) If a<0, it has maximum point at ...

#### Solution Summary

This is a series of problems involving parabolas, quadratic functions, and maximum product.

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