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The quadratic formulaThe quadratic formula

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This sample is an excerpt from one presentation on The Quadratic Formula in Boardworks High School Algebra I, which contains 46 interactive presentations in total.

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Information

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Any quadratic equation of the form ax2 + bx + c = 0 can be solved by substituting the values of a, b and c into the formula:

x =–b ± b2 – 4ac

2a

This equation can be derived by completing

the square on the general form of

the quadratic equation.

The quadratic formula

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Completing the square

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Using the quadratic formula

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The roots of a graph

We can demonstrate each of these possibilities using graphs.

Remember, if we plot the graph of y = ax2 + bx + c, the solutions to the equation ax2 + bx + c = 0 are given by the points where the graph crosses the x-axis.

y

x

b2 – 4ac is zero

one solution

y

x

b2 – 4ac is negative

no real solution

y

x

b2 – 4ac is positive

two solutions

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Using b2 – 4ac

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