3.3 Converting Standard & Vertex Forms

3.3 Converting Standard & Vertex Forms

Standard Form

 $\longrightarrow$  Vertex Form

• Factor out "a" and draw squares

• Complete the square with $\left(\frac{b}{2}\right)^2$  and balance outside

• Factor the perfect square and combine like terms

Multiple Choice

Match the equivalent quadratic function.

 $y=x^2+10x+35$  

•  $y=\left(x+5\right)^2+10$  

•  $y=2\left(x+2\right)^2+6$  

•  $y=\left(x-5\right)^2-10$  

•  $y=2\left(x-2\right)^2+6$  

Multiple Choice

Lets try another one. These are the hardest in my opinion. What do you think?

Match the equivalent quadratic function.

 $y=2x^2+8x+14$  

•  $y=\left(x+5\right)^2+10$  

•  $y=2\left(x+2\right)^2+6$  

•  $y=\left(x-5\right)^2-10$  

•  $y=2\left(x-2\right)^2+6$  

Vertex Form

 $\longrightarrow$  Standard Form

• Multiply binomial (F.O.I.L.)

• Distribute "a" value

• Combine like terms

Multiple Choice

Match the equivalent quadratic function.

 $y=\left(x-5\right)^2+10$  

•  $y=2x^2+20x+30$  
  

•  $y=x^2+10x+35$  
  

•  $y=x^2-10x+35$  

•  $y=x^2-10x+25$  

Root Form

 $\longrightarrow$  Standard Form

• Multiply binomial (F.O.I.L.)

• Distribute "a" value

• Combine like terms

Multiple Choice

Match the equivalent quadratic function.

 $y=2\left(x-1\right)\left(x+3\right)$  

•  $y=2x^2+4x-6$  
  

•  $y=x^2+2x-3$  
  

•  $y=x^2-2x-3$  

•  $y=2x^2-4x-6$