Parabolas in Vertex Form: Sample Test
1.
by ChemistNATE
(Nathan Oldridge)
Rewrite each of the following in vertex form.
2
a)
y=2 x −20 x+33
b)
y=−4 x −8 x+6
2
2
2.
A soccer ball's height (in metres) is h=−d +6 d +4
from where it was kicked.
at a horizontal distance of d metres
a)
What is the maximum height of the soccer ball? What is the horizontal distance this
corresponds to?
b)
What is the soccer ball's height, at a horizontal distance of 5 metres from where it was
kicked?
3.
Graph each of the following parabolas.
2
a)
y=(x+7) −4
b)
y=−x −8 x−10
2
4.
Write down the details of each function as requested (do not sketch)
2
y=6( x−17) +82
1
2
y=− ( x+2) −12
3
2
y=−(x+7) −4
Opens
(up/down)
Vertex
Stretch/Comp
Equation of
Axis of
Symmetry
Horizontal
Shift
Vertical Shift
5.
Describe the transformations applied to y=x2 in order to graph. Do not actually graph.
a)
1
2
y=− (x−7) +6
2
b)
y=−7( x+5) −1
c)
3 2
y= x −4
4
d)
y=(x+9)
2
2
6.
Give the equation for the graph of y=x2 after each of the following transformations:
a)
stretched by 3 vertically
translated 4 right
translated 9 down
b)
reflected in the x-axis
translated by 3 left
translated 6 up
c)
compressed by 3/4 vertically
translated 7 up
d)
reflected in the x-axis
stretched by 7 vertically
translated 8 right
7.
Graph the equation you
found in 6(b) above.
...you should have gotten
y = -(x+3)2+6
Answers
Practice Test for Maxi: Vertex Form
1.
a)
Rewrite each of the following in vertex form.
2
y=2 x −20 x+33
2
y=2(x −10 x)+33
2
y=2(x −10 x+25−25)+33
2
y=2(x−5) −50+33
y=2( x−5)2−17
b)
2
y=−4 x −8 x+6
2
y=−4(x +2 x)+6
2
y=−4(x +2 x+1−1)+6
2
y=−4(x+1) +4+6
y=−4( x+1)2+10
2
2.
A soccer ball's height (in metres) is h=−d +6 d +4
from where it was kicked.
at a horizontal distance of d metres
a)
What is the maximum height of the soccer ball? What is the horizontal distance this
corresponds to?
2
h=−(d −6 d )+4
2
h=−(d −6 d +9−9)+4
2
h=−(d−3) +9+4
2
h=−(d−3) +13
b)
So the maximum height is 13 meters
which is reaches at a horizontal distance of 3 m.
What is the soccer ball's height, at a horizontal distance of 5 metres from where it was
kicked?
Since horizontal distance is “d”, we just plug in 5 for “d”.
h=−(5) 2+6(5)+4
=−25+30+4
So it is at a height of 9 m
=9
3.
a)
Graph each of the following parabolas.
2
y=(x+7) −4
Vertex at (-7,-4)
Step pattern: 1,3,5,7
Over 1, Up 1 to (-6,-3)
Over 1, Up 3 to (-5,0)
Over 1, Up 5 to (-4,5)
b)
2
y=−x −8 x−10
Complete the square to find vertex
2
y=−( x +8 x)−10
2
=−( x +8 x+16−16)−10
2
=−( x+4) +16−10
y=−( x+4)2+6
Vertex at (-4,6)
Step pattern:
Over 1, Down 1 to (-3,5)
Over 1, Down 3 to (-2,2)
Over 1, Down 5 to (-1,-3)
Over 1, Down 7 to (0,-10)
4.
Write down the details of each function as requested (do not sketch)
y=6( x−17) +82
1
2
y=− ( x+2) −12
3
y=−(x+7) −4
up
down
down
(17,82)
(-2,-12)
(-7,-4)
2
Opens
(up/down)
Vertex
Stretch/Comp
Stretched vertically by 6
2
Compressed vertically by 1/3 Not stretched or compressed
Equation of
Axis of
Symmetry
x=17
x=-2
x=-7
Horizontal
Shift
17 right
2 left
7 left
Up 82
Down 12
Down 4
Vertical Shift
Describe the transformations applied to y=x2 in order to graph. Do not actually graph.
5.
1
2
y=− (x−7) +6
2
a)
•
•
•
•
2
y=−7( x+5) −1
b)
•
•
•
•
reflected vertically (“in x-axis”)
stretched vertically by 7
shifted left 5
shifted 1 down
3 2
y= x −4
4
c)
•
•
compressed vertically by 3/4
shifted down 4
2
d)
6.
Reflected vertically (“in x-axis”)
Compressed vertically by ½
Shifted right 7
Shifted up 6
y=(x+9)
•
shifted left 9
Give the equation for the graph of y=x2 after each of the following transformations:
a)
stretched by 3 vertically
translated 4 right
translated 9 down
y=3(x−4)2−9
b)
reflected in the x-axis
translated by 3 left
translated 6 up
y=−(x+3)2+6
c)
compressed by 3/4 vertically
translated 7 up
3 2
y= x +7
4
d)
reflected in the x-axis
stretched by 7 vertically
translated 8 right
y=−7( x−8)2
7.
Graph the equation you found in 6(b) above.
Vertex at (-3,6)
Step Pattern:
Over 1, Up 1 to (-2,7)
Over 1, Up 3 to (-1,10)