Using Quadratic Equations

Using the quadratic equation

Solve by completing the square

 $x^2+4x+3=0$  

Solve

 $ax^2+bx+c=0\$  

• by completing the square

•  $x^2+\frac{bx}{a}+\frac{c}{a}=0$  

•  $x^2+\frac{bx}{a}=-\frac{c}{a}$  

•  $\left(x+\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2=-\frac{c}{a}$  

•  $\left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}$  

•  $\left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}$  

•  $\left(x+\frac{b}{2a}\right)^2=\frac{b^2}{4a^2}-\frac{c}{a}$  

•  $\left(x+\frac{b}{2a}\right)^2=\frac{b^2}{4a^2}-\frac{4ac}{4a^2}$  

•  $x+\frac{b}{2a}^{ }=\pm\sqrt{\frac{b^2-4ac}{4a^2}}$  

•  $x+\frac{b}{2a}^{ }=\pm\frac{\sqrt{b^2-4ac}}{2a^{ }}$  

•  $x+\frac{b}{2a}^{ }=\pm\frac{\sqrt{b^2-4ac}}{2a^{ }}$  

•  $x^{ }=-\frac{b}{2a}\pm\frac{\sqrt{b^2-4ac}}{2a^{ }}$  

•  $x^{ }=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

Use the quadratic formula to solve:

 

 $x^2+4x+2=0$ 

Multiple Choice

What are a,b and c for

$$x^2\ +5x\ =2$$  

• a=1
  b=5
  c=2

• a=0
  b=5
  c=2

• a=1
  b=5
  c=-2

• a=1
  b=-5
  c=-2

Multiple Choice

What are a,b and c for

$$x^2-5x-2=0$$  

• a=1
  b=5
  c=2
  

• a=1
  b=-5
  c=-2

• a=0
  b=-5
  c=-2

• a=1
  b=-5
  c=2

Multiple Choice

What are a, b and c for

$$x^2-2x+5=0$$  

• a=1
  b=2
  c=5

• a=1
  b=-2x
  c=5

• a= $$1x^2$$  
  b=-2x
  c=5

• a=1
  b= -2
  c= 5

Multiple Choice

What is a, b and c for

$$2x^2+5x+3=0$$  

• a= $$2x^2$$  
  b=5x
  c=3

• a=1
  b=5
  c=3
  
  

• a=2
  b=5
  c=3

• a=2x
  b=5x
  c=3

Multiple Choice

What are a b and c for

$$x^2+4x\ +2=0$$  

• a=0
  b=4
  c=2

• a=1
  b=4
  c=2

• a=1
  b=4x
  c=2

• a=1 $$x^2$$  
  b=4x
  c=2