Unpacked Content
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.
- 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:
- Take the square root of both sides of an equation.
- Factor quadratic expressions in the form x2+bx+c where the leading coefficient is one.
- Use the factored form to find zeros of the function.
- Complete the square.
- Use the quadratic formula to find solutions to quadratic equations.
- Manipulate equations to rewrite them into other forms.
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).
Vocabulary
- quadratic equation
- Square root
- Factoring
- Completing the square
- quadratic formula
- Derive
- Real numbers
- Imaginary numbers
- Complex numbers
