Sample quiz on transformations of $y=x^2$
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1. For all quadratics, the parent function is usually taken as $\cdots$?
   
   $y=-x^2$
   $y=-2x^2$
   $y=2x^2$
   $y=x^2$
   
2. Relative to the parent $y=x^2$, what transformation produces $y=-x^2$?
   
   reflection in the $x$-axis
   reflection in the $y$-axis
   horizontal translation of $1$ unit left
   vertical translation of $1$ unit down
3. If the parent quadratic $y=x^2$ is reflected in the $y$-axis, what is the equation of the resulting quadratic?
   
   $y=-x^2$
   $y=(-x)^2$
   $y=-2x^2$
   $y=(-2x)^2$
4. Find the image of the point $(2,4)$ after the parent quadratic $y=x^2$ has been stretched vertically by a factor of $5$
   
   $(10,20)$
   $(2,20)$
   $(2,25)$
   $(10,16)$
5. Find the image of the point $(-3,9)$ if $y=x^2$ is compressed vertically by a factor of $\frac{2}{3}$, then translated $1$ unit up
   
   $(-3,7)$
   $(-3,6)$
   $(-2,7)$
   $(-2,6)$
6. The quadratic $y=(x-1)^2$ can be obtained from the parent $y=x^2$ through which transformation?
   
   horizontal translation of $1$ unit to the left
   horizontal translation of $1$ unit to the right
   vertical translation of $1$ unit up
   vertical translation of $1$ unit down
7. The quadratic $y=(x+2)^2$ can be obtained from the parent $y=x^2$ through which transformation?
   
   horizontal stretch by a factor of $2$
   horizontal compression by a factor of $\frac{1}{2}$
   horizontal translation of $2$ units to the left
   horizontal translation of $2$ units to the right
8. If the parent quadratic $y=x^2$ is stretched vertically by a factor of $5$, what is the resulting equation?
   
   $y=5x^2$
   $y=\frac{1}{5}x^2$
   $y=-5x^2$
   $y=x^2+5$
9. If the parent quadratic $y=x^2$ is stretched vertically by a factor of $3$, then translated $2$ units to the left, what is the new equation?
   
   $y=3(x-2)^2$
   $y=2(x+3)^2$
   $y=3(x+2)^2$
   $y=2(x-3)^2$
10. If the parent quadratic $y=x^2$ is stretched vertically by a factor of $4$, then translated $3$ units down, the vertex of the new quadratic is:
    
    $(4,-3)$
    $(4,3)$
    $(0,3)$
    $(0,-3)$
11. Find the vertex of the quadratic that results from compressing $y=x^2$ vertically by $\frac{1}{5}$ then translating horizontally $4$ units to the right.
    
    $(4,\frac{1}{5})$
    $(4,0)$
    $(-4,0)$
    $(-4,\frac{1}{5})$
12. Which of the following points remains unchanged after $y=x^2$ is stretched vertically by a factor of $3$?
    
    $(0,0)$
    $(1,1)$
    $(2,4)$
    $(3,9)$
13. Comparing $y=2x^2-2$ with the parent $y=x^2$, what are the transformations?
    
    vertical compression by $\frac{1}{2}$ and horizontal translation of $2$ units left
    vertical stretch by $2$ and vertical translation of $2$ units down
    vertical stretch by $2$ horizontal translation of $2$ units right
    vertical compression by $\frac{1}{2}$ and vertical translation of $2$ units up
14. If the vertex of $y=x^2$ becomes $(2,5)$, two possible transformations could be $\cdots$?
    
    horizontal translation of $2$ units right and vertical translation of $5$ units up
    horizontal translation of $2$ units right and vertical translation of $5$ units down
    horizontal translation of $5$ units right and vertical translation of $2$ units up
    horizontal translation of $5$ units left and vertical translation of $2$ units up
15. If $y=x^2$ is stretched vertically by a factor of $3$, translated horizontally $5$ units to the right, then translated vertically $7$ units down, what is the new equation?
    
    $y=3(x+5)^2-7$
    $y=3(x-5)^2+7$
    $y=3(x+5)^2+7$
    $y=3(x-5)^2-7$
16. If $y=x^2$ is stretched vertically by a factor of $4$, reflected in the $x$-axis, then translated vertically $6$ units down, what is the new equation?
    
    $y=-4(x-6)^2$
    $y=-4x^2+6$
    $y=-4x^2-6$
    $y=-6x^2-4$
17. If $y=x^2$ is stretched vertically by a factor of $4$, translated horizontally $5$ units to the right, then translated vertically $6$ units down, what is the vertex of the resulting quadratic?
    
    $(4,-6)$
    $(6,-4)$
    $(4,-5)$
    $(5,-6)$
18. If $y=x^2$ is stretched vertically by a factor of $2$, reflected in the $x$-axis, then translated vertically $8$ units up, what is the vertex of the new quadratic?
    
    $(0,8)$
    $(8,0)$
    $(0,-2)$
    $(8,-2)$
19. If $y=x^2$ is compressed vertically by a factor of $\frac{1}{4}$, translated horizontally $5$ units to the right, then translated vertically $7$ units down, what is the new equation?
    
    $y=4(x-5)^2-7$
    $y=\frac{1}{4}(x+5)^2-7$
    $y=4(x+5)^2+7$
    $y=\frac{1}{4}(x-5)^2-7$
20. If $y=x^2$ is compressed vertically by a factor of $\frac{1}{3}$, reflected in the $x$-axis, translated horizontally $3$ units to the right, then translated vertically $5$ units up, what is the new equation?
    
    $y=-\frac{1}{3}(x+3)^2+5$
    $y=-\frac{1}{3}(x-3)^2+5$
    $y=-\frac{1}{3}(x+5)^2+3$
    $y=-\frac{1}{3}(x-3)^2-5$