Review #2 Quadratics and Exponentials
Graphing Equations: Substitute values for x and solve for y….
Right triangles: (Short leg)2 + (Long leg)2 = (Hypotenuse)2
Equations for growth: y = Initial Value (1 + r)x where r is the decimal of %
Y = Initial value (1 + r/n)nt where n is the number of times per year
Equations for decay:
y = Initial value (1 – r)x where r is the decimal of %
Examples:
90,000 increases by 7.2% each year 90000(1 + .072)x
90,000 increase yearly by 5% monthly 90000(1 + .05/12)(12x)
50,000 (1.0006)(3/4) x increases .00006 / (3/4) or _____ each year
20,000 decreases by 3.4% a year 20,000(1-.034)x
Quadratic Equations: y = (x – root1)(x – root2)
Increasing: x<-.8 or x>2.1 (x values)
Decreasing: -.8 < x < 2.1
(x values)
Domain: All Real
Range:
All Real
End behavior: As x increases, y increases;
As x decreases, y decreases
1-3) Graph the following functions (without a calculator)
1) Y = 3x2 – 2x – 1
2) y = 3(2)x
3) 2x – 3y = 6
4) The cost of a house appreciates by 5.6% each year in a neighborhood from 2000-2008. The cost of the
house was $120,000 in 2000.
a) Write an equation that models this behavior
b) Find the cost of the house in 2008.
c) Suppose the actual cost of the house was $140,000 in 2008. Find the residual.
d) Suppose that the house appreciated 4% each ½ year. What would the new equation be?
e) What is the practical domain and range?
5) A car’s value is given by the equation: y = 20,000(.845)x where x is the value since 2010
a) What does the 20,000 represent?
b) By what percentage is the car depreciating at?
c) When is the car expected to be ½ of it’s initial value?
d) What is the predicted cost for 2014?
e) What is the practical domain and range from 2010-2017?
6) The height of a ball is given by the equation: h(t) = -4.9x2 + 12x + 6.
a) Suppose the ball was thrown 10 feet higher. What would the new equation be?
b) What does h(1) represent? Find it.
c) What does h(x) = 20 represent? Find it.
d) What is the maximum height?
e) How many seconds does it take the ball to hit the ground?
f) At what time is the ball the same height that it is thrown from?
g) What is the practical domain and range?
7) The larger leg of a right triangle is 8 less than four times the shorter leg. The hypotenuse is 8 more than the
shorter leg. Find the dimensions of the right triangle.
8) Write the quadratic function that has the roots -1/2 and 7
9) The cost of an antique appreciates by 4.2% each year from 2005-2012. The value of the antique is $800 in
2005.
a) Write an equation that models this behavior.
b) Find the value of the antique in 2008.
c) Suppose another antique dealer calculated the value of the antique to be y = 800(1.02)3/5x. Find the
difference in yearly rate.
10) A computer’s value decreases by 12.5% a year. The value in 2012 is $700
a) Write an equation that models this behavior
b) Find the predicted cost of 2014.
c) What is the practical domain and range?
11) The height of a ball is given by the equation: h(t) = -4.9x2 + 15x + 7.
a) Suppose the ball was thrown 3 feet lower lower. What would the new equation be?
b) What does h(1) represent? Find it.
c) What does h(x) = 12 represent? Find it.
d) What is the maximum height?
e) How many seconds does it take the ball to hit the ground?
f) At what time is the ball the same height that it is thrown from?
12) A company earns a weekly profit of P dollars by selling x items as modeled by the function:
P(x) = -x2 + 10x – 20
a) Find the zeros of the graph and give the interpretation.
b) How many items does the person need to sell to make a profit?
c) How many items does the person need to sell to maximize the profit?
13) The shorter leg is two less the larger leg. The hypotenuse is six less than twice the larger leg. Find the
shorter leg.
14) Write the quadratic function that has roots of 2 and -4
15) Graph the following equation. Identify the vertex, x-intercepts, y-intercept, end behavior, domain and
range. y = -2x2 + 8x – 2
Vertex
x-intercept:
y-intercept:
End behavior:
Domain:
Range:
16) Graph the following exponential equation identifying the y-intercept, end behavior, domain and range:
Y = 8(1/2)x
y-intercept:
End behavior:
Domain:
Range:
Exponentials
 Read carefully. These questions only require you
to plug in numbers.
 Be sure that you change % to a decimal (6.5% is
.0065)

CALCULATOR: ^ this command makes exponents
Ex: y = 5(4)x when x = 3
= 5*(4)^3
= 320
Example: In the formula A= P(1+ r)t, P is the principal, r is
the annual rate of interest, and A is the amount after t
years. Chen deposits $3,800 into a savings account that
pays 3.5% interest. About how much money will be left
in the account after 3 years?
P=3800 r= .035 t = 3
A=3800(1+.035)3
= $4213.00
Quadratics
Time is Always X
CALCULATOR: Y1  equation,Y2  height
Types of questions:
 How long does it take to hit the ground?
Ground is height=0. Y2 =0 [2nd] [TRACE]-> 5:intersect.

(scroll to x-axis where equation crosses) ENTER ENTER
ENTER
 What is the height after 1.5 seconds?
nd

[2nd] [WINDOW]->TblSt=1.5->[2
] [GRAPH] find answer
 How long will it take for the height to be 9 feet?
Y2 =9 [2nd] [TRACE]-> 5:intersect. (scroll to where 2
lines cross there should be 2 answers!! What goes up
must come down)
Ex: y  2x  6x  8
How long does it take to hit the ground?
-2x2 + 6x + 8 = 0
4 seconds
What is the height after 1.5 seconds?
Look at table for x = 1.5 12.5 feet

How long will it take for the height to be 9 feet?
-2x2 + 6x + 8 = 9
0.177 seC.& 2.82 seconds
Solve:
Y1=Left side of equation Y2 = right side of equation
(Roots = Xintercept= x is 0)
 [2nd] [TRACE]-> 5:intersect. (scroll to where 2 lines
cross there should be 2 answers!!)
2


Ex: Solve x
2
 3x
 5  33
x=-4 or x=7
1. Use the formula A  P(1 r) , P is the principal, r is
the annual rate of interest, and A is the amount after t
years. An account earning interest at a rate of 8% has a
principal of $350,000. If no more deposits or withdrawals
are made,
 approximately how much money will be in the
account after seven years?
A. $600,000 B. $2,142,800 C. $413,000 D.$515,000
t
2. Suppose a ball is dropped, use the formula h  7(0.6)
where h is the height and n is the number of bounces.
What is the height of the ball after 2 bounces?
A. 3.5 in.
B. 7.5 in.
C. 8.4 in. D. 2.5 in.

3. The number of laptops sold, y (in thousands), from 1998
x
to 2009 can be modeled by y  0.734(1.65) , where is
the number of years since 1998. According to the
equation, approximately how many laptops were sold in
2005?
A. 24.5 B. 24,500
 C. 9,000 D. Overflow
4A. In the formula A= P(1+ r)t, P is the principal, r is annual
rate of interest, and A is the amount after t years. Bobby
deposits $12,300 into a savings account that pays 2.4%
interest. About how much money will be left in the
account after 4 years?
A. $13,800 B. $50,380 C. $29,080 D. $13,520
4B. Suppose that the value, V, of a used car can be
calculated by using the formula
n  , where P

V  P 1  
 15 
represents the price of a new car and n represents years.
Jody purchased a new car for $17,000. The value of the car
is now $6,800. How old is the car?
A. 5 years B. 7 years C. 9 years D. 11 years
5. The formula h(t )  9.8t  3t  12 is used to find
the height (in ft). Find the height of the swimmer after 0.3
seconds.
A. 5 ft. B. 12 ft C. 10 ft D. 15ft
2
6. If the equation h  9.8t  20t  150 represents the
path of a rocket launched. When will the rocket hit the
ground?
A. 1 second B. 2 seconds C. 4 seconds D. 5 seconds
2
7. Solve x  12 x  28  7
A. {5, -7} B. {-5, -7} C. {-5,7} D. {5,7}
2
8. What are the roots of 16a  81  y ?
A. {9/4} B. {+9/4} C. {4/9} D. {+4/9}
2
9. What are the approximate solutions of x  3 x  8
(round to 1 decimal place)?
A. {1.7}
B. {No solution} C. {1.7, -4.7} D.
10. A ball is launched and follows the equation h(t) = -4.9t2
+ 15t + 3 where h(t) is height in meters and t is the time in
seconds. When is the height of the ball 2 meters?
A. 1.4 seconds B. 3.1 seconds C. 4.3 seconds D. 5.1 seconds
2

n