Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a ? 1), as equivalent expressions in completed square form, a(x - h)2 + k. They build quadratic expressions in basic business application contexts and rewrite them in equivalent forms.

Teacher and Student versions of full lesson from engageNY

Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw conclusions about the properties of irrational numbers, including closure for the irrational number system under various operations

Students derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax^2 + bx + c = 0, and use it to verify the solutions for equations from the previous lesson for which they have already factored or completed the square.

Students use the quadratic formula to solve quadratic equations that cannot be easily factored. Students understand that the discriminant, b2 - 4ac, can be used to determine whether a quadratic equation has one, two, or no real solutions.