MA19.A1.9
Select an appropriate method to solve a quadratic equation in one variable.
Select an appropriate method to solve a quadratic equation in one variable.
UP:MA19.A1.9
Vocabulary
- Completing the square
- Quadratic equations
- Quadratic formula
- Inspection
- Imaginary numbers
- Binomials
- Trinomials
Knowledge
Students know:
- 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 b2-4ac is less than zero.
Skills
Students are able to:
- Accurately use properties of equality 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.
Understanding
Students understand that:
- 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 used to produce the two solutions to the quadratic equation.
- Whether the roots of a quadratic equation are real or complex is determined by the coefficients of the quadratic equation in standard form (ax2+bx+c=0).
