Mastering the Completing the Square Technique

What is the standard form of a quadratic equation?

• ax^2 = bx + c

• ax^2 + bx = c

• ax + b = 0

• ax^2 + bx + c = 0

How do you solve a quadratic equation by factoring?

• Move all terms to one side of the equation

• Find two numbers that add to b and multiply to ac

• Take the square root of both sides

• Divide each term by the leading coefficient

What is the purpose of completing the square?

• To simplify the equation for graphing

• To eliminate the x term

• To transform the quadratic into a perfect square trinomial

• To find the discriminant

What is the first step in completing the square?

• Rearrange the equation to move the constant term to the right

• Add the square of half the coefficient of x to both sides

• Factor the quadratic completely

• Take the square root of both sides

How do you find the term to add to both sides when completing the square?

• sqrt(b^2 - 4ac)

• b^2 - 4ac

• 2a

• (b/2)^2

What do you do after adding (b/2)^2 to both sides?

• Factor the left side into a binomial square

• Solve for x directly

• Subtract the constant term from both sides

• Divide everything by a

How do you solve a completed square equation?

• Graphing

• Taking the square root of both sides

• Using the quadratic formula

• By factoring

What does the solution x = -1 ± sqrt(8) represent?

• No solution

• Two imaginary solutions

• One real solution

• Two real solutions

When completing the square results in a negative under the square root, what type of solutions do you get?

• Real and distinct

• Real and equal

• No solutions

• Imaginary

What is the form of the solution when dealing with imaginary numbers in completing the square?

• x = ± sqrt(b^2 - 4ac)

• x = a ± bi

• x = a/b ± sqrt(c)

• x = -b ± sqrt(b^2 - 4ac)/2a