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Wednesday 24th of May
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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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You have learned four ways to solve a quadratic equation:

â€¢ The Square Root Property

â€¢ Factoring

â€¢ Completing the square

You can solve any quadratic equation by completing the square or by using the quadratic formula. However, for some quadratic equations, it is quicker to solve by factoring or by using the Square Root Property.

When you want to solve a quadratic equation, try the following strategies:

1. Use the Square Root Property when the equation can be easily written in the form x2 = a or (x + k)2 = a.

 For example, the Square Root Property is useful for solving this equation: Add 16 to both sides. (x + 3)2 - 16 = 0 (x + 3)2 = 16 Use the Square Root Property to write two linear equations. Simplify each square root. Subtract 3 from both sides of each equation. x + 3 = 4 or x + 3 = -4 x =1 or x = -7

2. If the Square Root Property cannot be easily applied, write the equation in standard form, ax2 + bx + c = 0.

If the trinomial can be easily factored, solve the equation by factoring.

 For example, this strategy is useful for solving this equation: Add 6 to both sides of the equation. Factor the trinomial. Set each factor equal to 0. Solve each equation. x2 - 5x = -6 x2 - 5x + 6 = 0 (x - 2)(x - 3) = 0 x - 2 = 0 or x - 3 = 0 x = 2 or x = 3
3. The quadratic formula can be used to solve any quadratic equation, including the equations in the two previous examples.
 For example, the quadratic formula is useful for solving this equation: x2 + 1 = -5x To write the equation in standard form, add 5x to both sides of the equation. x2 + 5x + 1 = 0 Use the quadratic formula with a = 1, b = 5, and c = 1. Substitute the values for a, b, and c into the quadratic formula. Simplify.