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Common Core Standard HSA-REI.B.4a Questions

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

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Grade 10 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
To solve [math]x^2 + 8x + 16 = 25[/math] by using the square root property, how should you first rewrite the equation?
  1. [math](x+4)^2=25[/math]
  2. [math](x+4)^2=5[/math]
  3. [math]x^2+8x-9=0[/math]
  4. [math]x^2+8x=9[/math]
Grade 10 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which equation has the same solutions as [math]x^2 + 6x - 7 = 0[/math]?
  1. [math](x + 3)^2 = 2[/math]
  2. [math](x - 3)^2 = 2[/math]
  3. [math](x - 3)^2 = 16[/math]
  4. [math](x + 3)^2 = 16[/math]
Grade 9 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a, HSF-IF.C.8, HSF-IF.C.8a
If you complete the square for [math]x^2-10x=14[/math], what will the factored quadratic be?
  1. [math](x-5)^2=39[/math]
  2. [math](x-5)^2=114[/math]
  3. [math](x+5)^2=114[/math]
  4. [math](x+5)^2=39[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which of the following would be a correct step in completing the square to solve for the roots?
[math]x^2-24x+80[/math]
  1. [math](x-12)^2=64[/math]
  2. [math](x-12)^2=sqrt64[/math]
  3. [math](x-12)^2=sqrt(-64)[/math]
  4. [math](x-12)^2=-64[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which of the following would be a correct step in completing the square to solve for the roots?
[math]x^2+4x+29[/math]
  1. [math](x+2)^2=5i[/math]
  2. [math]x+2=pm5i[/math]
  3. [math](x-2)^2=pmsqrt(-25)[/math]
  4. [math](x-2)^2=-25[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which of the following would be a correct step in completing the square to solve for the roots?
[math]x^2-8x-48[/math]
  1. [math]x^2-4=sqrt64[/math]
  2. [math]x^2-4=64[/math]
  3. [math](x-4)^2=64[/math]
  4. [math](x-4)^2=sqrt64[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which of the following would be a correct step in completing the square to solve for the roots?
[math]x^2+6x+34[/math]
  1. [math]x=-3+-5i[/math]
  2. [math]x^2+6x+34=25[/math]
  3. [math]x^2+6x+9=25[/math]
  4. [math]x=5i+-3[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4a
Which of the following would be a correct step in completing the square to solve for the roots?
[math]x^2+2x-13[/math]
  1. [math]x^2+1=14[/math]
  2. [math](x+1)^2=sqrt14[/math]
  3. [math](x+1)^2=14[/math]
  4. [math]x^2+1=+-14[/math]

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