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IM Alg1.7.16 Lesson: The Quadratic Formula

Each expression represents two numbers. Evaluate the expressions and find the two numbers.

Choose one equation to solve, either by rewriting it in factored form or by completing the square. Be prepared to explain your choice of method.







Here is a formula called the quadratic formula.

The formula can be used to find the solutions to any quadratic equation in the form of , where , and  are numbers and  is not 0. This example shows how it is used to solve , in which , and . Here are some quadratic equations and their solutions. Use the quadratic formula to show that the solutions are correct. . The solutions are  and .

. The solutions are  and .

. The solutions are .

The solutions are .

.  The solution is .

. The solutions are  and .

Use the quadratic formula to solve . Let’s call the resulting equation P.

Solve the equation  in two ways, showing your reasoning for each:

  • Without using any formulas.

  • Using equation P.

Check that you got the same solutions using each method.

Use the quadratic formula to solve . Let’s call the resulting equation Q.

Solve the equation  in two ways, showing your reasoning for each:

  • Without using any formulas.

  • Using equation Q.

Check that you got the same solutions using each method.