identify the axis of symmetry, maximum or minimum value

Chapter 03 Test Name:_______________________

Date:_______________________

______________________________________________________________________________

1 What is the rate of change for the interval between A and B?

A

B

C 0D 1

2 Identify the axis of symmetry, maximum or minimum value, and the domain and range ofthe function.

y= –x2 + 2x + 2

A

axis of symmetry: maximum: 3domain: all real numbersrange: all real numbers < 3

B

axis of symmetry: maximum: 1domain: all real numbersrange: all real numbers < 1

C

axis of symmetry: maximum: 3domain: all real numbers < 3range: all real numbers

D

axis of symmetry: maximum: 3domain: all real numbersrange: all real numbers 3

______________________________________________________________________________________________Copyright © 2005 - 2006 by Pearson Education of 22

Chapter 03 Test ______________________________________________________________________________

3 Identify the axis of symmetry, maximum or minimum value, and the domain and range ofthe function.

y = 2x2 + 8x – 3

A

axis of symmetry: ;minimum: –11;domain: all real numbers > range: all real numbers

B

axis of symmetry: ;minimum: –11;domain: all real numbersrange: all real numbers >

C

axis of symmetry: ;minimum: –2;domain: all real numbersrange: all real numbers >

D

axis of symmetry: ;minimum: –11;domain: all real numbersrange: all real numbers

4 Rewrite the equation in vertex form. Identify the vertex and the axis ofsymmetry of the graph.

A vertex: axis of symmetry:

B vertex: axis of symmetry:

C vertex: axis of symmetry:

D vertex: axis of symmetry:

5 Write the expression in factored form.

x2 + 2x – 8

ABCD


Chapter 03 Test ______________________________________________________________________________


2x2 – 6x – 8

AB 2CD


ABCD


Chapter 03 Test ______________________________________________________________________________

8 Compare the equation, , the graph below, and the table below. Which has thesteepest rate of change from x = 1 to x = 2, and what is its value?

x y

–1 0

1 2

2 0

3 –4

A graph, –1B equation, –3

C table,

D equation,


Chapter 03 Test ______________________________________________________________________________

9 Write the equation of the parabola in vertex form. Identify the maximum or minimum value.

A maximum: 3

B maximum: 2

C maximum: 2

D maximum: –3


Chapter 03 Test ______________________________________________________________________________

10 Which graph represents two quadratic functions that are reflections of each other over thex-axis?

A

B

C

D


Chapter 03 Test ______________________________________________________________________________

11 Suppose you have the graph of .a. If you translate the parabola to the right 2 units and down 7 units, what is the equation ofthe new parabola in vertex form?b. If you translate the original parabola to the left 2 units and up 7 units, what is theequation of the new parabola in vertex form?c. How could you translate the new parabola in part (a) to get the new parabola in part (b)?

Aa.b.c.left 0 units, down 14 units

Ba.b.c.left 4 units, down 24 units

Ca.b.c.left 4 units, up 14 units


Chapter 03 Test ______________________________________________________________________________

12 What is the quadratic function with the given vertex and through the given point? Write theequation of the parabola in vertex form and describe how the function was transformed

from the parent function .vertex , point

A

; The parent function is compressed by a factor of .

B

; The parent function is stretched by a factor of 2.


Chapter 03 Test ______________________________________________________________________________

13 Graph the quadratic function. Identify the axis of symmetry, the vertex, and thedomain and range of the function.

A

vertex: ( , 2)axis of symmetry: domain: all real numbersrange: all real numbers

B

vertex: (3, )axis of symmetry: domain: all real numbersrange: all real numbers


Chapter 03 Test ______________________________________________________________________________

C

vertex: (3, 2)axis of symmetry: domain: all real numbersrange: all real numbers

D

vertex: ( , )axis of symmetry: domain: all real numbers range: all real numbers

14 Factor the expression completely.

ABCD


Chapter 03 Test ______________________________________________________________________________

15 Factor the expression completely.

AB

C

D

16 Solve the quadratic equation.

x2 – 9 = 0

A 3B –3C –6, –3D 3, –3


9x2 + 6x + 1 = 4

A

B

C

D


x2 + 2 = 0

A 2, –2

B

C i, –i

D 2i, –2i


Chapter 03 Test ______________________________________________________________________________

19 Solve the system of equations.

A (3, )(5, )

B ( , )( , )

C ( , 98)( , 150)

D ( , )( , )


Chapter 03 Test ______________________________________________________________________________

20 Solve the system of inequalities.

A

B

C


Chapter 03 Test ______________________________________________________________________________

D

21 Evaluate the discriminant of the equation. Determine the number and type of solutions.

x2 – 6x + 2 = 0

A 2 real solutionsB 1 real solutionC 2 imaginary solutionsD 1 imaginary solution

22 Evaluate the discriminant of the equation. Determine the number and type of solutions.

–2x2 + 7x = 10

A 2 imaginary solutionsB 1 imaginary solutionC 2 real solutionsD 1 real solution

23 The function models the height y, in feet, of your pet frog’s jump, where xis the horizontal distance, in feet, from the start of the jump. How far did the frog jump?How high did it go? Round your answer to the nearest tenth.

A The frog jumped about 3.2 ft far and about 22.9 ft high.B The frog jumped about 22.9 ft far and about 11.5 ft high.C The frog jumped about 22.9 ft far and about 3.2 ft high.D The frog jumped about 11.5 ft far and about 3.2 ft high.


Chapter 03 Test ______________________________________________________________________________

24 Identify the vertex, focus, and directrix of the parabola. Then graph the parabola.

A

vertex (4, 2); focus ; directrix

B

vertex (4, 2); focus ; directrix

C

vertex ( 4, 2); focus ; directrix


Chapter 03 Test ______________________________________________________________________________

D

vertex ( 4, 2); focus ; directrix

25 Write an equation for the parabola with the vertex (0, 0) and focus (5, 0).

A

B

C

D

26 Write an equation that models the given graph.

A (x + 3)2 + (y + 1)2 = 3B (x + 1)2 + (y + 3)2 = 6C (x – 3)2 + (y – 1)2 = 9D (x – 1)2 + (y – 3)2 = 3


Chapter 03 Test ______________________________________________________________________________

27 Write an equation in standard form of the circle with the center (0, 0) and radius 4.

A (x – 4)2 + y2 = 1B x2 + y2 = 16C x2 + y2 = 8D x2 + (y– 4)2 = 1

28 Without graphing, describe how the graph of the given equation differs from the graph of

.

A It compresses the graph of and reflects the graph across the x-axis.B It stretches the graph of .C It compresses the graph of .D It translates the graph of to the right 5 units.

29 Without graphing, describe how the graph of the given equation differs from the graph of

.

A It stretches the graph of and reflects it across the x-axis.B It compresses the graph of and reflects it across the x-axis.C It compresses the graph of .D It translates the graph of to the left 1.2 units.


Chapter 03 Test ______________________________________________________________________________

30 Write an equation for x2 + y2 = r2 translated left 3 units and up 2 units, with the radius 10.Then graph the equation.

A

(x + 3)2 + (y– 2)2 = 100

B

(x – 3)2 + (y + 2)2 = 100

C

(x + 2)2 + (y– 3)2 = 100


Chapter 03 Test ______________________________________________________________________________

D

(x – 2)2 + (y+ 3)2 = 100

31 Write the standard form of the equation for the circle that passes through the point and whose center is at the origin.

A

B

C

D

32 Identify the focus and the directrix of the graph of the equation

A focus (0, 7), directrix at y = 4B focus (0, 7), directrix at y = 4

C focus , directrix at y =

Dfocus , directrix at y =


Chapter 03 Test ______________________________________________________________________________

33 Write an equation of a parabola with its vertex at the origin and the given characteristics.

focus (0, 4)

A

B y= 4x2

C y= x2

D

34 Write an equation of a parabola with its vertex at the origin and the given characteristics.

directrix x =

A

B

C

D


Chapter 03 Test ______________________________________________________________________________

35 Find the center and the radius of the circle. Then choose the correct graph.

A

center (3, 5), radius 3

B

center ( , ), radius 3

C

center ( , 5), radius 3


Chapter 03 Test ______________________________________________________________________________

D

center ( , ), radius 3


identify the axis of symmetry, maximum or minimum value

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