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Unit 9A Review: Quadratics

Authored by Kristie Sosnowski

Mathematics

9th - 12th Grade

CCSS covered

Used 3+ times

Unit 9A Review: Quadratics
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7 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Solve by factoring.

 x23x=0x^2-3x=0  

0

3

0,3

-3

Answer explanation

 x23x=0x^2-3x=0  
 x(x3)=0x\left(x-3\right)=0  
 x=0, x3=0x=0,\ x-3=0 

  x=0, x=3x=0,\ x=3  

Tags

CCSS.HSA-REI.B.4B

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Write the equation in standard form given the roots:

 34,1\frac{3}{4},-1  

 x=34,   x=1x=\frac{3}{4},\ \ \ x=-1  

 (x34)(x+1)=0\left(x-\frac{3}{4}\right)\left(x+1\right)=0  

 x2+14x34=0x^2+\frac{1}{4}x-\frac{3}{4}=0  

 4x2+x3=04x^2+x-3=0  

Answer explanation


 x=34, x=1x=\frac{3}{4},\ x=-1  
 x34=0,     x+1=0x-\frac{3}{4}=0,\ \ \ \ \ x+1=0  
 (x34)(x+1)=0\left(x-\frac{3}{4}\right)\left(x+1\right)=0  
Multiply the first binoial by 4 to clear the fraction.

 (4x3)(x+1)=0\left(4x-3\right)\left(x+1\right)=0  
 4x2+4x3x3=04x^2+4x-3x-3=0  
 4x2+x3=04x^2+x-3=0  

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve by COMPLETING THE SQUARE.

 3x212x+6=03x^2-12x+6=0  

 ±2\pm\sqrt{2}  

 2±22\pm\sqrt{2}  

 2-2  

 4, 04,\ 0  

Answer explanation

 3x212x+6=03x^2-12x+6=0  
Divide ALL terms by 3.

 x24x+2=0x^2-4x+2=0  
set up the framework.  Move 2 to the other side.

 x24x+=2+x^2-4x+\ldots\ldots=-2+\ldots\ldots  
 42=(2)2=4-\frac{4}{2}=\left(-2\right)^2=4  Add 4 to both sides.

 x24x+4=2+4x^2-4x+4=-2+4  
 (x2)2=2\left(x-2\right)^2=2   Take the square root of both sides.
 x2=±2x-2=\pm\sqrt{2}  
 x=2±2x=2\pm\sqrt{2}  

Tags

CCSS.HSA-REI.B.4B

4.

FILL IN THE BLANK QUESTION

2 mins • 1 pt

Find the value of the discriminant.

 7x2+6x+2=07x^2+6x+2=0  

Answer explanation

 7x2+6x+2=07x^2+6x+2=0  

 a=7, b=6, c=2a=7,\ b=6,\ c=2  
 (6)24(7)(2)\left(6\right)^2-4\left(7\right)\left(2\right)  
 3656=2036-56=-20  

Tags

CCSS.HSA-REI.B.4B

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If the discriminant is the value of 19, describe the type of root(s).

real, rational

real, irrational

complex

Tags

CCSS.HSA-REI.B.4B

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve the quadratic inequality and write your answer in interval notation.


 x2+3x18x^2+3x\ge18  

 (,6][3,)\left(-\infty,-6\right]\cup\left[3,\infty\right)  

 (,6)(3,)\left(-\infty,-6\right)\cup\left(3,\infty\right)  

 [6,3]\left[-6,3\right]  

 (6,3)\left(-6,3\right)  

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve with any method.
 2x2+8x+22=02x^2+8x+22=0  


 x=2±i7x=-2\pm i\sqrt{7}  

 x=8±4i74x=\frac{-8\pm4i\sqrt{7}}{4}  

No real solutions

 x=2±7x=-2\pm\sqrt{7}  

Answer explanation

 2x2+8x+22=02x^2+8x+22=0  
 x2+4x+11=0x^2+4x+11=0  
 x2+4x+=11+x^2+4x+\ldots=-11+\ldots  
 x2+4x+4=11+4x^2+4x+4=-11+4  
 (x+2)2=7\left(x+2\right)^2=-7  
Take the square root of both sides.
 x+2=±7x+2=\pm\sqrt{-7}  
 x=2±i7x=-2\pm i\sqrt{7}  

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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