Intro to Quadratic Equations.

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Presentation transcript:

Intro to Quadratic Equations

What are we trying to do? At least get the equation into quadratic form; often solve for x. 2x2 = 3x – 1 2x2 - 3x + 1 = 0 This might be as far as we can get – but we always want to get at least this far. If possible, factor it further: (2x – 1)(x – 1) = 0

Solving (2x – 1)(x – 1) = 0 What do we do to solve? Each binomial can be treated as a separate term. When we multiply two things together and they equal 0, one of them must be 0. Thus, we set each binomial equal to 0 and solve.

Solving (2x – 1)(x – 1) = 0 First binomial: 2x – 1 = 0 2x = 1 x = ½ Second Binomial: x – 1 = 0 x = 1 So x = 1, ½

What if it doesn’t factor? Quadratic formula: For any quadratic equation where ax2 + bx + c = 0 (-b +/- √(b2-4ac))/2a We aren’t doing that today, but we’ll be deriving this later this week.