Algebra II Transformations of Quadratics Quiz

Write an equation for a parabola given:

vertical compression (shrink) magnitude 1/2, translate 2 units left and 5 units down.

• $f\left(x\right)=-\frac{1}{2}\left(x+2\right)^2-5$

• $f\left(x\right)=-\frac{1}{2}\left(x-2\right)^2-5$

• $f\left(x\right)=\frac{1}{2}\left(x+2\right)^2-5$

• $f\left(x\right)=\frac{1}{2}\left(x-2\right)^2-5$

Select all transformations that map

 $f\left(x\right)=x^2$  onto  $g\left(x\right)=-2\left(x-1\right)^2+3$  

• Reflect across the x-axis

• Vertical compression magnitude 2

• Vertical stretch magnitude 2

• Horizontal translation 1 unit right

• Vertical translation 3 units up

Is the vertex of the parabola  $f\left(x\right)=2\left(x-4\right)^2-1$  a maximum or a minimum value?

Select all that apply:
The parabola is symmetric about the line  $x=1$  

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

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

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

•  $f\left(x\right)=-2\left(x-1\right)^2-5$  

Write the equation for the parabola g(x) graphed above.

Feel free to use the magnifier to see the graph better.

• $g\left(x\right)=\left(x-4\right)^2-5$

• $g\left(x\right)=-\left(x-4\right)^2+5$

• $g\left(x\right)=-\left(x+4\right)^2+5$

• $g\left(x\right)=\left(x+4\right)^2+5$