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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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 Ineq. #4:

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 Solve for:

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Most text books provide a nice proof of the quadratic formula. To derive the two
solutions for any quadratic equation we simply solve by completing the
square. This guide will focus on using the formula to solve problems.

 Quadratic Formula: If where a≠0 then
 Solve: Step 1: Identify a, b and c. Step 2: Write down the formula. Step 3: Plug in the appropriate values and evaluate.

The argument of the square root is called the discriminant and can be used to
determine the number and type of solutions to the quadratic equation without doing all
the work to find the actual solutions.

 Using the discriminant to determine the types of solutions - If <0(negative) then there are two nonreal complex solutions If = 0(zero) then there is one real solution If>0 If (positive) then there are two real solutions

In the last problem and we got two real solutions.

A. Use the Discriminant to determine the number and type of solutions.

B. Solve using the quadratic formula.

If the discriminant is a perfect square then the quadratic was factorable. In this case, it is
usually faster to solve by factoring and should be done that way unless stated otherwise.

C. Solve using the quadratic formula.