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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 (xp)2 = q that has the same solutions. Derive the quadratic formula from this form.

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Factor the quadratic trinomial $x^2+19x+70$.
1. $(x-14)(x-5)$
2. $(x-15)(x-4)$
3. $(x+15)(x+4)$
4. $(x+14)(x+5)$
Factor the quadratic trinomial $w^2-8w-84$.
1. $(w-14)(w-6)$
2. $(w+14)(w+6)$
3. $(w-14)(w+6)$
4. $(w+14)(w-6)$
What is the factored form for the quadratic trinomial $x^2+8x+15$.
1. $(x-3)(x-5)$
2. $(x+3)(x+5)$
3. $(x-3)(x+5)$
4. $(x+3)(x-5)$
Factor the quadratic trinomial $k^2+28k+196$.
1. $(k-14)(k-14)$
2. $(k+14)(k+14)$
3. $(k+14)(k-14)$
4. $(k+14i)(k+14i)$
Factor the quadratic trinomial $x^2-10x+25$.
1. $(x-5)(x-5)$
2. $(x+5)(x+5)$
3. $(x−5)(x+5)$
4. $(x-5i)(x-5i)$
Find the a, b, and c for this quadratic equation: $-6x^2-12=0$
1. $a=-6, b =0, and c=-12$
2. $a=6, b = 0, and c= 12$
3. $a=0, b= 12, and c =-6$
4. $a= -12, b=-6, and c= 0$
Factor the quadratic trinomial $64m^2-81n^2$.
1. $(8m-9n)(8m+9n)$
2. $(8m+9n)(8m+9n)$
3. $(8m-9n)(8m-9n)$
4. $(8m-9ni)(8m+9ni)$
Factor the quadratic trinomial $169d^2-121$.
1. $(13d−11)(13d-11)$
2. $(13d−11i)(13d+11i)$
3. $(13d+11)(13d+11)$
4. $(13d−11)(13d+11)$
Which of the following would be a correct step in completing the square to solve for the roots?
$x^2-24x+80$
1. $(x-12)^2=64$
2. $(x-12)^2=sqrt64$
3. $(x-12)^2=sqrt(-64)$
4. $(x-12)^2=-64$
Which of the following would be a correct step in completing the square to solve for the roots?
$x^2+4x+29$
1. $(x+2)^2=5i$
2. $x+2=5i$
3. $(x-2)^2=sqrt(-25)$
4. $(x-2)^2=-25$
Which of the following would be a correct step in completing the square to solve for the roots?
$x^2-8x-48$
1. $x^2-4=sqrt64$
2. $x^2-4=64$
3. $(x-4)^2=64$
4. $(x-4)^2=sqrt64$
Which of the following would be a correct step in completing the square to solve for the roots?
$x^2+6x+34$
1. $x=-3+-5i$
2. $x^2+6x+34=25$
3. $x^2+6x+9=25$
4. $x=5i+-3$
$x^2+2x-13$
1. $x^2+1=14$
2. $(x+1)^2=sqrt14$
3. $(x+1)^2=+-14$
4. $x^2+1=+-14$