UP:MA19.8A.11

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.

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.

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).