evident square roots by Quadratic equations square root of a real number manipulations including taking square inspection, then so is -a, roots of both sides of an equation, Quadratic formula Transform quadratic equations to The method for completing the Accurately complete the square on a a form where the square root of square, quadratic polynomial as a strategy for Complex solutions each side of the equation may be finding solutions to quadratic taken, including completing the equations, Notational methods for Inspection square, expressing complex numbers, Factor quadratic polynomials as a Use the method of completing strategy for finding solutions to A quadratic equation in the square on the equation in quadratic equations, standard form (ax2+bx+c=0) standard form (ax2+bx+c=0) to has real roots when b2-4ac is derive the quadratic formula, greater than or equal to zero Rewrite solutions to quadratic and complex roots when equations in useful forms including a ± Identify quadratic equations is less than zero. and simplified radical expressions, bi which may be solved efficiently by factoring, and then use Make strategic choices which factoring to solve the equation, procedures (inspection, completing the square, factoring, and quadratic Use the quadratic formula to formula) to use to reach a solution to a solve quadratic equations, quadratic equation. Explain when the roots are real Solutions to a quadratic equation must or complex for a given quadratic make the original equation true and equation, and when complex this should be verified, write them as for real a ± bi numbers and a b, When the quadratic equation is derived from a contextual situation, proposed Demonstrate that a proposed solutions to the quadratic equation solution to a quadratic equation should be verified within the context is truly a solution by making the given, as well as mathematically, original true. Different procedures for solving quadratic equations are necessary under different conditions, If ab=0, then at least one of a or b must be zero (a=0 or b=0) and this is then
evident square roots by inspection, Transform quadratic equations to a form where 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 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. 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 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, Different procedures for solving quadratic equations are necessary under different conditions, If ab=0, then at least one of a or b must be zero (a=0 or b=0) and this is then
Algebra-1-Pacing-Guide-Version-3.docx