Quadratics Review!
I can find the parts of a quadratic
1) Find the parts of the quadratics in vertex form:
a) 𝑓(𝑥) = 2 (𝑥 – 3)2 – 4
b) 𝑓(𝑥) = 3 ( 𝑥 + 2)2 – 6
c) 𝑓(𝑥) = −3(𝑥 + 4)2 + 5
d) 𝑓(𝑥) = −2( 𝑥 + 5)2 + 1
e) 𝑓(𝑥) = ½ (𝑥 − 5)2 – 2
1
f) 𝑓(𝑥) = − 3 (𝑥 + 1)2 + 4
vertex
MAX/min
________
________
________
________
________
________
________
________
________
________
________
________
Value of
Max/Min
_________
_________
_________
_________
_________
_________
horizontal shift vertical shift
_________
_________
_________
_________
_________
_________
____________
____________
____________
____________
____________
____________
2) Identify the y-intercept for each function. (Intercepts are points & written as an ordered pairs!)
a) 𝑓(𝑥) = 𝑥 2 + 3𝑥 + 4 _____________
b) 𝑓(𝑥) = 2𝑥 2 – 4𝑥 – 5
_________________
c) 𝑓(𝑥) = (𝑥 + 2)2 + 3 ______________
e) 𝑓(𝑥) = 𝑥 2 + 4𝑥
______________
3) Find the zeroes for each equation:
a) y = x2 – 20
b) y = 2x2 + 5x
e) y = -2 (x+3)2 + 2
i) y =
 14 x  3  2x  1
m) f(x) = 6x2 + x – 12
d) 𝑓(𝑥) = 3(𝑥 − 1)2 – 7
_________________
f) 𝑓(𝑥) = −3(𝑥 − 2)(𝑥 + 4) __________________
c) y = x2 + 12x + 10
d) y = 3(x-2)2
g) y = x ( x-4)
h) y = (x-3) (x+7)
j) y = x2 – 2
k) y = x2 – 2x – 2
l) y = 6x2 – 15x – 36
n) f(x) = 2x2 –x – 15
o) f(x) = -2x2 +11x - 12
f) y =  x 

2 2
5
 64
25
4) Given the equation in standard form, identify the vertex and rewrite it in vertex form.
a) f(x) = x2 + 6x + 9
d) f(x) = 2x2 – 20x + 42
b) f(x) = x2 – 6x + 8
e) f(x) = 3x – 3x2 +6
5) Investigate the function: f(x) = – (x-1)2 + 9
a) What is the shape of the graph?
c) f(x) = 2x2 +12x + 10
f) f(x) = 2x2 – 20 x + 5
f)
Does the function open up or down? Maximum
or minimum? How do you know?
b) What is the type of function?
g) Write the x-intercepts.
c) In what form is the equation written?
h) Write the equation in standard form.
d) What is the equation for the axis of symmetry?
i)
What is the y-intercept?
j)
Graph of the function.
f)
Does the function open up or down? Maximum
or minimum? How do you know?
e) What is the vertex?
6) Investigate the function: f(x) = – 5x2 + 20x + 160
a) What is the shape of the graph?
b) What is the type of function?
g) Write the x-intercepts.
c) In what form is the equation written?
h) Write the equation in standard form.
d) What is the equation for the axis of symmetry?
e) What is the vertex?
i)
j)
What is the y-intercept?
Graph of the function.
I can write an equation of a quadratic.
7) Write the transformed equation g(x) in vertex form using the parent function f(x) = x 2.
a) translated 3 units down
& 5 units to the left
d) vertically compressed by a
factor of 1/3 and
reflected over the x-axis
g) translated 4 units down,
5 units to the right, & a
vertical stretch of ½
b) translated 4 units up
& 6 units to the right
e) translated 2 units up with a
vertical stretch of a factor of 4
h) translated 6 units to the left,
3 units up & a vertical
compression of ¾
8) Given the zeroes, write a quadratic function in standard form:
a) x = 2 and x = 4
b) x = -3 and x = 10
c) vertically stretched by a factor
of 2 and translated up 3
f) translated 3 units to the left
with a vertical compression of ½
i) reflected over the x-axis,
shifted 3 units to the left,
and 2 units down
c) x = 10 and x = - 8
I can convert between forms of quadratics:
9) Convert to vertex form:
a) f(x) = ( x – 4) ( x – 10)
b) f(x) = x2 – 20x – 40
c) f(x) = x2 – 12x + 32
d) f(x) = x2 + 8x +15
e) f(x) = 2x2 – 20 x + 9
I can solve application problems using quadratics.
10) A rocket is launched at an initial velocity of 64 ft/sec from a height of 6 feet. Use the equation h(t) = - 16t2 + vo t +
ho
a) Write the equation:
c) Determine how long it takes to reach the maximum
height to the nearest tenth of a second.
b) Find the maximum height in feet, to the nearest
tenth of a foot.
d) Determine when the rocket will hit the ground to the
nearest tenth of a second.
11) A rocket is launched at an initial velocity of 39.2 meters per second from a roof that is 10 meters high.
Use the equation h(t) = - 4.9t2 + vo t + ho
a) Find the maximum height to the nearest tenth of
b) Determine how long it takes to reach the
a meter.
maximum height, to the nearest tenth of a second.
c) Determine how long it takes to reach the ground, to the nearest tenth of a second.
12) You have a roll of fencing that is 48 yards and wish to enclose an area on all 4 sides.
a) Draw a diagram
b) Write an equation to show the area.
c) What are the dimensions that would give the largest area? (Rounded to the nearest tenth of a yard)
13) You are building a rectangular pen for a rabbit. The wire fencing is available in 20-foot roll. You are going to
purchase one roll of fencing.
a) Make a labeled diagram of the pen.
c) Find the maximum area (rounded to the nearest
b) Write an equation for the area.
tenth of a foot).
d) Give the dimensions of the pen.
14) You are going to make a picture frame. The length is 6 inches more than the width. The area should be
216 square inches. Find the dimensions of the frame rounded to the nearest tenth of an inch.