Solving Quadratic Equations with Rational Solutions

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

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.

• Rewrite as

  x² + bx = c

• Take half of b, square it, then

  add this to both sides.

• Factor the perfect square trinomial.

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

• 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.

• Rewrite as

  ax² + bx = c

• Divide the entire equation by a

• Take half of b, square it, then

  add this to both sides.

• Factor the perfect square trinomial.

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

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

• Make sure the equation is

  set equal to 0 and written

  in standard form.

  ax² + bx + c = 0

• Identify a, b, and c.

• Substitute these values

  into the formula

• Simplify using the order of operations

  (PEMDAS)

• Write the answer using curly braces in set notation

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

• bx

• square roots

• cx

• discriminant

• quadratic formula

• Isolate the

• Take the square root of both sides.

• Eliminate the

Ethan, Michael, and Benjamin are on a treasure hunt. They come across a mysterious door with a riddle that reads, 'What is the first step in solving a quadratic equation by factoring?'

• Set the equation equal to zero.

• Factor the equation completely.

• Find the discriminant of the equation.

• Solve for the variable in the equation.

Answer explanation

The first step in solving a quadratic equation by factoring is to set the equation equal to zero.

What is the quadratic formula used for?

• To find the solutions or roots of a quadratic equation.

• To find the sum of two numbers.

• To calculate the area of a triangle.

• To determine the slope of a line.

Answer explanation

The quadratic formula is used to find the solutions or roots of a quadratic equation.