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

Find the vertex by completing the square. Write your answer as an ordered pair with no spaces

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?