Solving Quadratic
Functions by
completing the
square
Applications of
quadratic
functions
$100
$100
$100
$100
$100
$200
$200
$200
$200
$200
$300
$300
$300
$300
$300
$400
$400
$400
$400
$400
$500
$500
$500
$500
$500
Solving Quadratic
Equations with Quadratic Formula
Square Roots
Classifying
Functions
Completing the square$100
Use completing the square to solve
2
a
+ 14a − 51 = 0
Write your answer in simplest radical form.
Completing the square $100
{3, −17}
Completing the square $200
Use completing the square to solve
2
x
+ 14x − 15 = 0
Write your answer in simplest radical form.
Completing the square $200
{1, −15}
Completing the square $300
Use completing the square to solve
2
k −
12k + 23 = 0
Write your answer in simplest radical form.
Completing the square $300
Completing the square - $400
2
5k
= 60 − 20k
Completing the square $400
{2, −6}
Completing the square - $500
2
8x +
16x = 42
Completing the square $500
Applications with quadratic functions $100
We are going to fence in a rectangular field and
we know that for some reason we want the field
to have an enclosed area of 75 ft2. We also know
that we want the width of the field to be 3 feet
longer than the length of the field. What are the
dimensions of the field? Round your answer to
the nearest tenth.
Applications with quadratic functions $100
So, we have one positive and one negative. From the stand point of needing the
dimensions of a field the negative solution doesn’t make any sense so we will
ignore it.
Therefore, the length of the field is 7.2892 feet. The width is 3 feet longer than this
and so is 10.2892 feet.
Applications $200
A ball is thrown straight up,
from 3 m above the ground, with
a velocity of 14 m/s. When does
it hit the ground? Use the
function h = 3 + 14t − 5t2 .
Applications $200
The "t = −0.2" is a negative time,
impossible in our case.
The "t = 3" is the answer we want:
The ball hits the ground after 3 seconds!
Applications $300
The height, , in feet of an object above the
ground is given by h = -16t2 + 64t +190
where t is the time in seconds. Find the time it
takes the object to strike the ground and find the
maximum height of the object.
Applications $300
Since t represents time, we must throw out –1.98.
.
Therefore,
it takes 5.98 seconds for the object to
strike the ground.
And at that time, the maximum height is 254 feet.
Application $400
A soccer ball bounces straight up into the air off of the
head of a soccer player form an altitude of 6 feet with
an initial velocity of 40 feet per second. Use the
function s = -16t2 + v0t + s0 to determine how long does
it take the ball to reach the earth?
Applications $400
2.6 seconds
Application $500
An object in launched directly
upward at 64 feet per second (ft/s)
from a platform 80 feet high. What
will be the object's maximum
height? When will it attain this
height?
Applications $500
It takes two seconds to
reach the maximum
height of 144 feet.
Solving Quadratic Equations with Square Roots- $100
4 x  6  230
2
Solving Quadratic Equations with Square Roots- $100
x  
59
Solving Quadratic Equations with Square Roots- $200
10  4v  154
2
Solving Quadratic Equations with Square Roots- $200
Solving Quadratic Equations with Square Roots- $300
7 x  1  47
2
Solving Quadratic Equations with Square Roots- $300
Solving Quadratic Equations with Square Roots- $400
8 p  2  382
2
Solving Quadratic Equations with Square Roots- $400
p  4
3
Solving Quadratic Equations with Square Roots- $500
100 x  9  16
2
Solving Quadratic Equations with Square Roots- $500
Quadratic Formula- $100
2v  64  8v
2
Write your answer in simplest radical form if needed
Quadratic Formula- $100
Quadratic Formula- $200
7n  11  0
2
Write your answer in simplest radical form if needed
Quadratic Formula- $200
Quadratic Formula- $300
8k  8  2k
2
Write your answer in simplest radical form if needed
Quadratic Formula- $300
Quadratic Formula- $400
2a  3a  11
2
Write your answer in simplest radical form if needed
Quadratic Formula- $400
Quadratic Formula- $500
2 x  3x  27
2
Quadratic Formula- $500
Classifying Functions- $100
Tell whether the table of
values represents a linear,
exponential, quadratic, or
Neither:
x
-2
-1
0
1
2
y
8
2
-4
-10
-16
Classifying Functions - $100
Linear Function
Classifying Functions - $200
Tell whether the table of
values represents a linear,
exponential, quadratic, or
Neither:
x
-2
-1
0
y
20
10
5
1
2
2.5 1.75
Classifying Functions- $200
Exponential Function
Classifying Functions - $300
Tell whether the table of
values represents a linear,
exponential, quadratic, or
Neither:
x
-2
-1
0
1
2
y
6
4
2
0
-2
Classifying Functions - $300
Linear
Classifying Functions - $400
Tell whether the table of
values represents a linear,
exponential, quadratic, or
Neither:
: 0 1 2
x
-2
-1
y
8
5
4
5
8
Classifying Functions - $400
Quadratic Function
Classifying Functions- $500
Tell whether the table of
values represents a linear,
exponential, quadratic, or
Neither:
x
-1
0
1
2
3
y
4
1
0
1
4
Classifying Functions- $500
Quadratic Function
END OF GAME
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