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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 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]x^2+19x+70[/math].
  1. [math](x-14)(x-5)[/math]
  2. [math](x-15)(x-4)[/math]
  3. [math](x+15)(x+4)[/math]
  4. [math](x+14)(x+5)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]w^2-8w-84[/math].
  1. [math](w-14)(w-6)[/math]
  2. [math](w+14)(w+6)[/math]
  3. [math](w-14)(w+6)[/math]
  4. [math](w+14)(w-6)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
What is the factored form for the quadratic trinomial [math]x^2+8x+15[/math]?
  1. [math](x-3)(x-5)[/math]
  2. [math](x+3)(x+5)[/math]
  3. [math](x-3)(x+5)[/math]
  4. [math](x+3)(x-5)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]k^2+28k+196[/math].
  1. [math](k-14)(k-14)[/math]
  2. [math](k+14)(k+14)[/math]
  3. [math](k+14)(k-14)[/math]
  4. [math](k+14i)(k+14i)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]x^2-10x+25[/math].
  1. [math](x-5)(x-5)[/math]
  2. [math](x+5)(x+5)[/math]
  3. [math](x−5)(x+5)[/math]
  4. [math](x-5i)(x-5i)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Find the a, b, and c for this quadratic equation: [math]-6x^2-12=0[/math]
  1. [math]a=-6, b =0, and c=-12[/math]
  2. [math]a=6, b = 0, and c= 12[/math]
  3. [math]a=0, b= 12, and c =-6[/math]
  4. [math]a= -12, b=-6, and c= 0[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]64m^2-81n^2[/math].
  1. [math](8m-9n)(8m+9n)[/math]
  2. [math](8m+9n)(8m+9n)[/math]
  3. [math](8m-9n)(8m-9n)[/math]
  4. [math](8m-9ni)(8m+9ni)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSA-REI.B.4a
Factor the quadratic trinomial [math]169d^2-121[/math].
  1. [math](13d−11)(13d-11)[/math]
  2. [math](13d−11i)(13d+11i)[/math]
  3. [math](13d+11)(13d+11)[/math]
  4. [math](13d−11)(13d+11)[/math]
Grade 11 Quadratic Equations and Expressions CCSS: 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.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.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.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.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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