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Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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THE QUADRATIC FORMULA

Definition:

• Quadratic Equation: is an equation that can be written in the form

where a, b, and c are real numbers, a ≠ 0.

Important Properties:

• Quadratic Formula: The solutions of ax^2 + bx + c = 0 where a ≠ 0 are given by

• The quadratic formula is a result of solving ax^2 + bx + c = 0 by completing the square.
• The quadratic formula can be used to solve any quadratic equation.
• If b^2 - 4ac < 0 then there are no real solutions to the quadratic equation.
• If b^2 - 4ac = 0, then the quadratic equation has only one real zero.
• If b^2 - 4ac > 0, then the quadratic equation has two real solutions

Common Mistakes to Avoid:

• Before identifying a, b, and c to be used in the quadratic formula, make sure one side of your equation
is zero.
• In the quadratic formula, the -b is also divided by 2a.