When we are faced with a quadratic that is not “nice” to factor we need to find a way to factor it. This is where the quadratic formula comes in. The discriminant is a value that can be calculated for each quadratic equation. Depending on the value of the discriminant, we can determine if the quadratic equation has a solution, or has factors, or not.
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Solving linear relationships involves determining what the value of the variable is. I will usually tell students the first step is to move everything with a variable on one side of the equal sign and all the numbers to the other side of the equal sign.