Quadratic equations Solve quadratic equations where Any real number has two Accurately use properties of equality both sides of the equation have Quadratic formula square roots, that is, if a is the (Table 4) and other algebraic evident square roots by square root of a real number manipulations including taking inspection, then so is -a, square roots of both sides of an Complex solutions equation, Transform quadratic equations to The method for completing the Inspection a form the square root of square, Accurately complete the square on a each side of the equation may be quadratic polynomial as a strategy taken, including completing the for finding solutions to quadratic Notational methods for square, equations, expressing complex numbers, Use the method of completing the Factor quadratic polynomials as a A quadratic equation in square on the equation in standard strategy for finding solutions to standard form (ax2+bx+c=0) form (ax2+bx+c=0) to derive the quadratic equations, has real roots when b2-4ac is quadratic formula, greater than or equal to zero and complex roots when Rewrite solutions to quadratic Identify quadratic equations is less than zero. equations in useful forms including a which may be solved efficiently and simplified radical ± bi by factoring, and then use expressions, factoring to solve the equation, Make strategic choices about which Use the quadratic formula to procedures (inspection, completing solve quadratic equations, the square, factoring, and quadratic formula) to use to reach a solution to a quadratic equation. Explain when the roots are real or complex for a given quadratic equation, and when complex Solutions to a quadratic equation write them as for real must make the original equation true a ± bi numbers and and this should be verified, a b, Demonstrate that a proposed When the quadratic equation is solution to a quadratic equation is derived from a contextual situation, truly a solution by making the proposed solutions to the quadratic original true. equation should be verified within the context given, as well as mathematically,
Solve quadratic equations where both sides of the equation have evident square roots by inspection, Transform quadratic equations to a form the square root of each side of the equation may be taken, including completing the square, Use the method of completing the square on the equation in standard form (ax2+bx+c=0) to derive the quadratic formula, Identify quadratic equations which may be solved efficiently by factoring, and then use factoring to solve the equation, Use the quadratic formula to solve quadratic equations, Explain when the roots are real or complex for a given quadratic equation, and when complex write them as a ± bi for real numbers a and b, Demonstrate that a proposed solution to a quadratic equation is truly a solution by making the original true. Quadratic equations Quadratic formula Complex solutions Inspection Any real number has two square roots, that is, if a is the square root of a real number then so is -a, The method for completing the square, Notational methods for expressing complex numbers, A quadratic equation in standard form (ax2+bx+c=0) has real roots when b2-4ac is greater than or equal to zero and complex roots when is less than zero. Accurately use properties of equality (Table 4) and other algebraic manipulations including taking square roots of both sides of an equation, Accurately complete the square on a quadratic polynomial as a strategy for finding solutions to quadratic equations, Factor quadratic polynomials as a strategy for finding solutions to quadratic equations, Rewrite solutions to quadratic equations in useful forms including a ± bi and simplified radical expressions, Make strategic choices about which procedures (inspection, completing the square, factoring, and quadratic formula) to use to reach a solution to a quadratic equation. Solutions to a quadratic equation must make the original equation true and this should be verified, When the quadratic equation is derived from a contextual situation, proposed solutions to the quadratic equation should be verified within the context given, as well as mathematically,
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