Quadratic Equations by Completing Squares

Which of the following are methods to solve quadratics (select all that apply)?

• Difference of Squares

• Completing the Square

• Square Roots

• Grouping

Tags

CCSS.HSA-REI.B.4B

Mike solved the equation x² + 8x = 14 by completing the square. Which of the following equations is part of the correct solution.

• (x + 4)² = 14

• x² + 8x - 14 = 0

• (x + 4)² = 30

• x² + 8x + 4 = 18

Tags

CCSS.HSA-REI.B.4B

What value of "c" would create a

perfect square trinomial?

x² + 10x + _____ = 17

• c = 20

• c = 100

• c = 25

• c = 10

Tags

CCSS.HSA-REI.B.4B

Which formula do you use to find the "c-value" that makes a quadratic a perfect square trinomial?

Tags

CCSS.HSA-REI.B.4B

What are the steps to solving this by completing the square?

• Take the square root of both sides of the equation

• Subtract 5 from both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

• Subtract 21 from both sides of the equation

Answer explanation

Steps for completing the square when a=1

1st: Rewrite as x² + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

Tags

CCSS.HSA-REI.B.4B

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

• Write the answer using curly braces in set notation

• 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.

Tags

CCSS.HSA-REI.B.4B

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.

• Factor the perfect square trinomial.

• Rewrite as

  ax² + bx = c

• Take half of b, square it, then

  add this to both sides.

• Divide the entire equation by a

Tags

CCSS.HSA-REI.B.4B

The points at which a parabola intersects the x-axis are the ________________.

• quadratic roots

• vertex

• axis of symmetry

• asymptotes

• factors

Tags

CCSS.HSF-IF.C.7A

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

• to check solutions

• QUADRATIC FORMULA

• when there is no "bx" term

• GRAPHING

• can be used in all cases

• FACTORING

• when the equation is factorable

• COMPLETING THE SQUARE

• when b is an even number if a=1

• SQUARE ROOTS

Tags

CCSS.HSA-REI.B.4B

What is another word for roots of an equations?

(Select all choices that apply.)

• y-intercepts

• zeros

• vertex

• x-intercepts

• solutions

Tags

CCSS.HSF-IF.C.7A