# Sample quiz on transformations of parabolas Main home here.

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?
$y=-\frac{1}{3}(x+3)^2+5$
$y=-\frac{1}{3}(x-3)^2+5$
$y=-\frac{1}{3}(x+5)^2+3$
$y=-\frac{1}{3}(x-3)^2-5$