Writing Quadratic Equations

Which of the following is the equation for a quadratic that shifts 2 units right, 4 units down, and has a vertical stretch of 2 from the parent function?

• $f\left(x\right)=2\left(x-2\right)^2-4$

• $f\left(x\right)=2\left(x+2\right)^2-4$

• $f\left(x\right)=\frac{1}{2}\left(x+2\right)^2-4$

Which of the following represent the function that has a vertex of (1, 4) and goes through the point (3, 6)?

• $f\left(x\right)=\frac{1}{2}\left(x-1\right)^2+4$

• $f\left(x\right)=\left(x-1\right)^2+4$

• $f\left(x\right)=\left(x+1\right)^2-4$

 Which of the following represent the quadratic that is shift 3 units left and 6 units up from the parent function $f\left(x\right)=x^2$ ?

•  $f\left(x\right)=\left(x+3\right)^2+6$  

•  $f\left(x\right)=\left(x-3\right)^2+6$  

•  $f\left(x\right)=\left(x+3\right)^2-6$  

•  $f\left(x\right)=\left(x-3\right)^2-6$  

Rewrite $f\left(x\right)=2\left(x+4\right)^2-10$ in standard form. 

•  $f\left(x\right)=2x^2+16x+22$  

•  $f\left(x\right)=x^2+8x+16$  

•  $f\left(x\right)=2x^2+22$  

Rewrite $f\left(x\right)=-\frac{1}{2}\left(x-2\right)^2+5$ in standard form. 

•  $f\left(x\right)=x^2-4x+4$  

•  $f\left(x\right)=-\frac{1}{2}x^2+2x+3$  

•  $f\left(x\right)=-\frac{1}{2}x^2+7$  

•  $f\left(x\right)=-\frac{1}{2}x^2+2x-7$