# Unit 2 Equivalent Expressions And Quadratic Functions 2013

**Topics:**Maxima and minima, Quadratic equation, Polynomial

**Pages:**16 (4164 words)

**Published:**July 1, 2015

Quadratic Functions

Radical Expressions

1) Express as a mixed radical in simplest form.

a)

c)

b)

e)

d)

f)

2) Simplify.

a)

b)

d)

e)

c)

f)

3) Simplify.

a)

b)

c)

d)

e)

f)

4) Simplify.

a)

d)

b)

e)

f)

c)

For questions 5 to 9, calculate the exact values and express your answers in simplest radical form. 5) Calculate the length of the diagonal of a square with side length 4 cm. 6) A square has an area of 450 cm2. Calculate the side length. 7) Determine the length of the diagonal of a rectangle with dimensions 3 cm

9 cm.

8) Determine the length of the line segment from A(-2, 7) to B(4, 1). 9) Calculate the perimeter and area of the triangle to the right. 10) If

and

, which is greatest,

or

?

11) Express each radical in simplest form.

a)

c)

b)

d)

12) Simplify

FMSS 2013

.

Page 1 of 16

Solutions

1a)

2a)

3a)

4a)

4e)

8)

11a)

1b)

1c)

1d)

2c) 32

2b)

3b)

3c)

4b)

1e)

2d)

3d)

9) Perimeter =

11b)

3e)

4c)

5)

4f)

1f)

2e)

cm

2f) -140

3f)

4d)

6)

units, Area = 12 square units 10)

11c)

11d) –

cm

7)

cm

12)

Polynomial Expressions

13) Expand and Simplify

a)

b)

c)

d)

e)

f)

14) Expand and Simplify

a)

b)

c)

d)

e)

f)

15) Expand and Simplify

a)

b)

d)

e)

16) Factor

a)

b)

c)

d)

e)

f)

17) Factor

a)

b)

c)

d)

e)

f)

18) Factor

a)

b)

c)

d)

e)

f)

19) Show that

and

are equivalent.

20) Show that

and

are not equivalent.

FMSS 2013

Page 2 of 16

21) a) Is

equivalent to

? Justify your decision.

b) Write a simplified expression that is equivalent to

.

22) Show that the expressions

and

are not equivalent.

23) Determine whether the functions in each given pair are equivalent. a)

and

b)

and

c)

and

e)

and

f)

and

g)

and

h)

and

24) The two equal sides of an isosceles triangle each have a length of . Determine the length of the third side.

. The perimeter of the triangle is

25) For each pair of functions, label the pairs as equivalent, non-equivalent, or cannot be determined. a)

c)

e)

for all values of in the domain

b)

d)

26) Halla used her graphing calculator to graph three different polynomial functions on the same axes. The equations of the functions appeared to be different, but her calculator showed only two different graphs. She concluded that two of her functions were equivalent.

a) Is her conclusion correct? Explain.

b) How could she determine which, if any, of the functions were equivalent without using her graphing calculator?

27) a) Consider the linear functions

and

. Suppose that

. Show that the functions must be equivalent.

b) Consider the two quadratic functions

and

,

,

. Show that the functions must be equivalent.

28) Is the equation

, and

. Suppose that

true for all, some, or no real numbers? Explain.

29) a) If

has two terms and

has three terms, how many terms will the product of

and

have

before like terms are collected?

b) In general, if two or more polynomials are to be multiplied, how can you determine how many terms the product will have before like terms are collected? Explain and illustrate with an example.

Solutions

3

2

2

2

2

2

2

13a) 25x + 15x – 20x 13b) 2x – 7x – 30 13c) 16x – 53 x + 33 13d) n – 13n + 72 13e) -68x – 52x – 2 13f) 5a – 26a – 37 3

3

2

3

2

3

2

3

2

14a) 4x – 100x 14b) -2a – 16a – 32a 14c) x – 5x – 4x + 20 14d) -6x + 31x – 23x – 20 14e) 729a – 1215a + 675a – 125 2

2

2

2

14f) a – 2ad – b + 2bc – c + d

4

3

2

2

3

6

4

3

2

2

15a) x + 4x + 2x – 4x + 1 15b) 8 – 12a + 6a – a 15c) x – x – 2x – 3x – 2x – 1 15d) -16x + 43x – 13 16a) (x -7)(x + 2) 16b) (x +5y)(x - y) 16c) 6(m -6)(m – 9) 16d) (2y +7)(y – 1)

16e) (4a – 7b)(2a + 3b) 16f) 2(2x + 5)(4x + 9)

4

2

17a) (x -3)(x + 3) 17b) (2n -7)(2n + 7) 17c) (x + 1)(x + 1)(x – 1)(x + 1) 17d)...

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