Unit 9A Review: Quadratics

Solve by factoring.

 $x^2-3x=0$  

• 0

• 3

• 0,3

• -3

Answer explanation

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

  $x=0,\ x=3$  

Tags

CCSS.HSA-REI.B.4B

Write the equation in standard form given the roots:

 $\frac{3}{4},-1$  

•  $x=\frac{3}{4},\ \ \ x=-1$  

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

•  $x^2+\frac{1}{4}x-\frac{3}{4}=0$  

•  $4x^2+x-3=0$  

Answer explanation

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

 $\left(4x-3\right)\left(x+1\right)=0$  
 $4x^2+4x-3x-3=0$  
 $4x^2+x-3=0$  

Solve by COMPLETING THE SQUARE.

 $3x^2-12x+6=0$  

•  $\pm\sqrt{2}$  

•  $2\pm\sqrt{2}$  

•  $-2$  

•  $4,\ 0$  

Answer explanation

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

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

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

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

Tags

CCSS.HSA-REI.B.4B

Find the value of the discriminant.

 $7x^2+6x+2=0$  

Answer explanation

 $7x^2+6x+2=0$  

 $a=7,\ b=6,\ c=2$  
 $\left(6\right)^2-4\left(7\right)\left(2\right)$  
 $36-56=-20$  

Tags

CCSS.HSA-REI.B.4B

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

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

 $x^2+3x\ge18$  

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

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

•  $\left[-6,3\right]$  

•  $\left(-6,3\right)$  

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

•  $x=-2\pm i\sqrt{7}$  
  

•  $x=\frac{-8\pm4i\sqrt{7}}{4}$  
  

• No real solutions

•  $x=-2\pm\sqrt{7}$  
  

Answer explanation

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

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7