Determine the Best Method of Solving Quadratic Equations

The ____________ is used to determine the number of solutions to a quadratic equation.

Order the following steps for solving quadratic equations by factoring.

• Set the quadratic equation equal to zero.

• Factor the left side.

• Write the answer using curly braces in set notation.

• Set each factor equal to zero, and solve each for the variable.

• bx

• square roots

• cx

• discriminant

• quadratic formula

• Isolate the

• Take the square root of both sides.

• Eliminate the

If you have a ​ (a)   , you can solve the quadratic equation by square roots!

Remember a ​ (b)   number always has ​ (c)   real square roots, so you must solve for both cases.

• difference of squares

• perfect square trinomial

• positive

• negative

• sum of cubes

• difference of cubes

• rational

• two

• one

• three

Reorder the following steps to solve a quadratic equation when the leading coefficient is 1 (a = 1) to solve the equation by completing the square.

• Factor the perfect square trinomial.

• Rewrite as

  x² + bx = c

• Take the square root of both sides and solve for both cases.

• Take half of b, square it, then

  add this to both sides.

• Write the answer using curly braces in set notation

Reorder the following steps to solve a quadratic equation when the leading coefficient is not 1 (a > 1) to solve the equation by completing the square.

• Take the square root of both sides and solve for both cases.

• Take half of b, square it, then

  add this to both sides.

• Factor the perfect square trinomial.

• Rewrite as

  ax² + bx = c

• Divide the entire equation by a

Reorder the following steps to solve a quadratic equation by using the quadratic formula.

• Identify a, b, and c.

• Simplify using the order of operations

  (PEMDAS)

• Substitute these values

  into the formula

• Write the answer using curly braces in set notation

• Make sure the equation is

  set equal to 0 and written

  in standard form.

  ax² + bx + c = 0

Match the following methods to solve quadratic equations with the scenario it is best used in

• can be used in all cases

• COMPLETING THE SQUARE

• when b is an even number if a=1

• FACTORING

• when there is no "bx" term

• QUADRATIC FORMULA

• when the equation is factorable

• GRAPHING

• to check solutions

• SQUARE ROOTS

When is a quadratic equation factorable?

• When the diagonal

  (ax=y) is a perfect square

• When the difference

  (d=ax²−c) is a perfect square

• When the difference

  (d=ax²−c) is a perfect cube

• When the discriminant

  (d=b²−4ac) is a perfect cube

• When the discriminant

  (d=b²−4ac) is a perfect square

Complete the quadratic formula in the diagram shown given that a quadratic equation is in standard form a x^2 + b x + c = 0,

a

b

c