Common Core · High school
HSA-REI.B.4.B
High school — Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring.
High school — Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, and recognise when the quadratic formula gives complex solutions and write them as a ± bi.
The 2 skills that cover it
- Quadratic EquationsSolve equations containing a squared term by factoring, by taking square roots, and with the quadratic formula.Read the lesson →
- Complex NumbersExtend the number system with i = sqrt(-1): simplify powers of i, add, subtract, multiply and divide complex numbers, and solve the quadratics whose discriminant is negative.Read the lesson →
What a student should be able to do
- Solve a quadratic by factoring and the zero-product property.
- Solve x2 = k by taking square roots, keeping both signs.
- Apply the quadratic formula and interpret the discriminant.
- Solve projectile and area word problems with quadratics.
- Write the square root of a negative number in terms of i, and simplify a power of i.
- Add, subtract and multiply complex numbers, and write the result in the form a + bi.
- Divide complex numbers by multiplying by the conjugate of the denominator.
- Solve a quadratic equation with a negative discriminant and write its complex solutions.