6.5 -- Completing the square

6.5 -- Completing the square

Steps:

• 1. Move c to the other side of the equal sign

• 2. Add

   $\left(\frac{b}{2}\right)^2$  to both sides of the equation

• 3. Factor the left side of the equation

Vertex form of a quadratic:

• (-h,k) is the vertex of the equation

• h is ALWAYS OPPOSITE

• After we complete the square, we can set the equation = to zero to get it in vertex form

Fill in the Blanks

Remember Factoring? Good times...

•  $x^2-8x+12$  

• Find 2 numbers that multiply to be 16 and add to be -8

•  $\left(x-6\right)\left(x-2\right)$  

• Set both factors = to zero and solve for the roots

•  $\left(x-6\right)=0;\ x=6$   $\left(x-2\right)=0;\ x=2$  

Students: UGH Mrs. Kuhlman this is really difficult

Mrs. Kuhlman: Have you tried graphing it with Desmos?