In this lesson, students solve basic quadratic equations using inspection and concrete examples. In the associated Algebra 1 lesson, students solve similar equations with less aid. By providing students with the concrete examples of area of squares and a list of possible solutions, students can begin to see patterns in the solutions so that they may more easily solve basic quadratic equations by inspection later. Students look for and make use of structure (MP7) when they encounter expressions such as and treat it as one quantity.
Explain (orally) why quadratic equations can have more than one solution.
Justify both positive and negative values of solutions to quadratic equations.
Solve quadratic equations by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as for real numbers and .