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ALGEBRA 1 EOC REVIEW 2 QUADRATICS AND EXPONENTIALS

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ALGEBRA 1

EOC REVIEW 2

QUADRATICS

AND

EXPONENTIALS

GRAPH THE FOLLOWING FUNCTION (WITHOUT A CALCULATOR).

y = 3 x2 – 2 x – 1

1)

1) Find the vertex.

y = 3(1/3)2 – 2(1/3) – 1

y = - 4/3

V = (1/3, - 4/3)

2) Plot other points.

3) Draw graph.

GRAPH THE FOLLOWING FUNCTION (WITHOUT A CALCULATOR).

y = 3 (2)x

2)

GRAPH THE FOLLOWING FUNCTION (WITHOUT A CALCULATOR).

2 x – 3 y = 6

3)

– 3 y = - 2 x + 6

y = 2/3 x – 2

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.

y = 120,000(1.056)x

b) Find the cost of the house in 2008.

$ 185,563.52

- Suppose the actual cost of the house was
- $ 140,000 in 2008. Find the residual.

$ 185,563.52 – 140,000 = $ 45,563. 52

d) Suppose that the house appreciated 4 % each ½ year. What would the new equation be?

y = 120,000(1.056)2x

e) What is the practical domain and range?

DOMAIN: x ≥ 0

RANGE: y ≥ 120,000

5)

A car’s value is given by the equation

y = 20,000 (.845)x where x is the years since 2010.

a) What does the 20,000 represent?

initial cost

b) By what percentage is the car depreciating?

15.5 %

- When is the car expected to be ½ of its initial value?

x = 4, 2014

d) What is the predicted cost for 2014?

$ 10,051.53

e) What is the practical domain and range from 2010 – 2017?

DOMAIN: x ≥ 0

RANGE: y ≤ 20,000

6)

The height of a ball is given by the equation:

h(t) = - 4.9 t2 + 12 t + 6.

a) Suppose the ball was thrown 10 feet higher. What would the new equation be?

h(t) = - 4.9 t2 + 12 t + 16

b) What does h(1) represent? Find it.

Height at 1 second. h(1) = 13.1 feet

- What does h(x) = 20 represent. Find it.

Time it takes to reach 20 feet. Doesn’t reach 20 feet

d) What is the maximum height?

13.34 feet

e) How many seconds does it take the ball to hit the ground?

2.875 seconds

f) At what time is the ball the same height that it is thrown from?

2.449 seconds

g) What is the practical domain and range?

DOMAIN: 0 ≤ x ≤ 3

RANGE: 6 ≤ y ≤ 13.34

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 lengths of the sides of the right triangle.

shorter leg: x

= 5

= 12

longer leg: 4 x – 8

= 13

hypotenuse: x + 8

x2 + (4 x – 8)2 = (x + 8)2

x2 + 16 x2 – 64 x + 64 = x2 + 16 x + 64

16 x2 – 64 x + 64 = 16 x + 64

16 x2 – 80 x = 0

{0, 5}

16 x(x – 5) = 0

8)

Write the quadratic function that has roots

- ½ and 7.

f (x) = (x + ½ )(x – 7)

f (x) = 2 (x + 1 )(x – 7)

f (x) = 2 (x2 – 6 x – 7)

f (x) = 2 x2 – 12 x – 14 )

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 the equation that models this behavior.

y = 800(1.042)x

b) Find the value of the antique in 2008.

y = 800(1.042)3 = $ 905.09

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.

(1.02)5/3 = 1.0335

1.0420 – 1.0335 = .0085

.85 %

10)

A computer’s value decreases by 12.5 % a year. The value in 2012 is $ 700.

a) Write the equation that models this behavior.

y = 700(.875)x

b) Find the predicted cost in 2014.

y = 700(.875)2 = $ 535.94

c) What is the practical domain and range?

DOMAIN: x ≥ 0

RANGE: 0 ≤ y ≤ 700

11)

The height of a ball is given by the equation:

h(t) = - 4.9 t2 + 15 t + 7.

a) Suppose the ball was thrown 3 feet lower. What would the new equation be?

h(t) = - 4.9 t2 + 15 t + 4

b) What does h(1) represent? Find it.

height after 1 second

h(t) = 17.1 feet

c) What does h(x) = 12 represent? Find it.

time it takes to reach 12 feet

.38 sec., 2.68 sec.

d) What is the maximum height?

18.47 feet

e) How many seconds does it take the ball to hit the ground?

3.47 seconds

f) At what time was the ball the same height that it was thrown from?

3.06 seconds

12)

A company earns a weekly profit of P dollars by selling x items as modeled by the function: P(x) = - x2 + 10 x – 20.

a) Find the zeros of the graph and give the interpretation.

2.76, 7.23

break-even points

b) How many items does the company need to sell to make a profit?

3 ≤ x ≤ 7

c) How many items does the company need to sell to maximize the profit?

5

13)

The shorter leg is two less than the larger leg. The hypotenuse is six less than twice the larger leg. Find the shorter leg.

shorter leg: x – 2

= 8 – 2 = 6

longer leg: x

= 8

hypotenuse: 2 x – 6

= 10

(x – 2)2 + x2 = (2 x – 6)2

x2 – 4 x + 4 + x2 = 4 x2 – 24 x + 36

- 2 x2 – 4 x + 4 = – 24 x + 36

- 2 x2 + 20 x + 4 = 36

- 2 (x – 8)(x – 2) = 0

- 2 x2 + 20 x – 32 = 0

{8, 2}

- 2 (x2 – 10 x + 16) = 0

14)

Write the quadratic function that has roots of 2 and - 4.

f(x) = (x – 2)(x + 4)

f(x) = x2 + 2 x – 8

15)

Graph the following equation. Identify the vertex, x-intercepts, y-intercept, end behavior, domain, and range. y = - 2 x2 + 8 x – 2 .

(2, 6)

vertex:

V(2, 6)

x-intercepts:

.268, 3.732

y-intercept:

- 2

end behavior:

As x dec., y dec.

As x inc., y dec.

domain:

All real numbers

range:

y ≤ 6

16)

Graph the following exponential equation. Identify the y-intercept, end behavior, domain, and range.

y = 8 (1/2)x.

8

y-intercept:

end behavior:

As x dec., y inc.

As x inc., y dec.

domain:

All real numbers

range:

y > 0

1)

Use 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. 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?

B) $ 2,142,800

A) $ 600,000

D) $ 515,000

C) $ 413,000

2)

Suppose a ball is dropped, use the formula:

h = 7(0.6)n where h is the height and n is the number of bounces. What is the height of the ball after 2 bounces?

B) 7.5 in.

A) 3.5 in.

D) 2.5 in.

C) 8.4 in.

3)

The number of laptops sold, y (in thousands), from 1998 to 2009 can be modeled by

y = 0.7341(1.65)x, where x is the number of years since 1998. According to this equation, approximately how many laptops were sold in 2005?

B) 24,500

A) 24.5

D) Overflow

C) 9,000

4)A

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. 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?

B) $ 50,380

A) $ 13,800

D) $ 13, 520

C) $ 29,080

4)B

Suppose that the value, V, of a used car can be calculated by using the formula

, where P 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?

B) 7 years

A) 5 years

D) 11 years

C) 9 years

5)

The formula h(t) = - 9.8 t2 + 3 t + 12 is used to find the height (in feet). Find the height of the swimmer after 0.3 seconds.

B) 12 feet

A) 5 feet

D) 15 feet

C) 10 feet

6)

If the equation h = - 9.8 t2 + 20 t + 150 represents the path of a rocket launched, when will the rocket hit the ground?

B) 2 seconds

A) 1 second

D) 5 seconds

C) 4 seconds

7)

Solve: x2 – 12 x + 28 = - 7

B) {- 5, - 7}

A) {5, - 7}

D) {5, 7}

C) {- 5, 7}

8)

What are the roots of 16 a2 – 81 = y?

B) {± 9/4}

A) {9/4}

D) {± 4/9}

C) {4/9}

9)

What are the approximate solutions of x2 + 3 x = 8? (Round to 2 decimal places.)

B) {No Solution}

A) {1.7}

D) {4.7}

C) {1.7, - 4.7}

A ball is launched and follows the equation h(t) = - 4.9 t2 + 15 t + 3 where h(t) is height in meters and t is time in seconds. When is the height of the ball 2 meters?

10)

B) 3.1 seconds

A) 1.4 seconds

D) 5.1 seconds

C) 4.3 seconds