Solving Quadratics by Completing the Square

Solving Quadratics by Completing the Square

The next 5 slides are based on recap from last lesson.

Multiple Select

 $b^2-4ac$  is called the?

• Quadratic Formula

• Discriminant

Multiple Select

What does it mean when  $b^2-4ac=0\ ?$  

• It has a repeated root

• It has a double root

• The graph will just touch the x axis

Multiple Select

Complete the square for  $x^2+4x$  

•  $\left(x+2\right)-4$  
  

•  $\left(x+2\right)^2-4$  
  

•  $\left(x+2\right)^2+4$  

Multiple Select

Complete the square for  $x^2-6x+15$  

•  $\left(x-3\right)^2-9+15$  
  

•  $\left(x+3\right)^2+6$  
  

•  $\left(x-3\right)^2+6$  

Multiple Select

Complete the square for  $x^2-5x+3$  

•  $\left(x-\frac{5}{2}\right)^2-\frac{13}{4}$  
  

•  $\left(x-\frac{5}{2}\right)^2-\frac{19}{2}$  
  

Let's check how you got on...

Multiple Select

Solve  $x^2+4x-2=0$   

•  $x=-2\pm\sqrt{6}$  

•  $-2\pm\sqrt{-2}$  

Multiple Select

Solve  $2x^2+6x-3=0$  

•  $x=-\frac{3}{2}\pm\frac{\sqrt{15}}{2}$  

•  $x=\ \frac{-3\pm\sqrt{15}}{2}$  

•  $\frac{1}{2}\left(-3\pm\sqrt{15}\right)$