Free Printable Lopez Unit 2B Review

1.

What is the name for this quadratic function?

a)

basic function

b)

parent function

c)

sister function

d)

Coach Lopez's function

2.

What is the equation for this quadratic function?

a)

$y=\left(x+2\right)^2$

b)

$y=2x$

c)

$y=x^2$

d)

$y+2=x$

3.

What is the vertex of the parent function?

a)

$y\ =\ x^2$

b)

(10, 10)

c)

0

d)

(0, 0)

4.

How has the new function (in red) transformed from the parent function?

a)

stretched by 3

b)

shifted down by 3

c)

reflected

d)

shifted right by 3

5.

What is the equation of the transformed function (in red)?

a)

$y\ =\ \left(x-3\right)^2$

b)

$y\ =\ \left(x+3\right)^2$

c)

$y\ =\ 3x$

d)

$y\ =\ x^2\ +\ 3$

6.

What is the vertex of the transformed function (in red)?

a)

(0, 0)

b)

(3, 0)

c)

(0, 3)

d)

(3, 3)

7.

How has the new function (in red) transformed from the parent function?

a)

stretched by 4

b)

shifted down by 4

c)

reflected

d)

shifted right by 4

8.

What is the equation of the transformed function (in red)?

a)

$y\ =\ \left(x-4\right)^2$

b)

$y\ =\ \left(x+4\right)^2$

c)

$y\ =\ -4x^2$

d)

$y\ =\ x^2\ -\ 4$

9.

What is the vertex of the transformed function (in red)?

a)

(0, 0)

b)

(4, 0)

c)

(0, -4)

d)

(-4, 0)

10.

How has the new function (in red) transformed from the parent function?

a)

compressed and reflected

b)

reflected and shifted down

c)

stretched and shifted down

d)

stretched and reflected

11.

What is a possible equation for the transformed function (in red)?

a)

$y\ =\ -x^2\ -\ 5$

b)

$y\ =\ -5x^2$

c)

$y\ =\ -\left(5-x\right)^2$

d)

$y\ =\ -\frac{1}{5}x^2$

12.

What is the vertex of the transformed function (in red)?

a)

(0, -5)

b)

(-5, 0)

c)

(0, 0)

d)

(5, -5)

13.

How has the new function (in red) transformed from the parent function?

a)

compressed

b)

reflected

c)

stretched

d)

shifted down

14.

What is a possible equation for the transformed function (in red)?

a)

$y\ =\ x^2\ -\ 9$

b)

$y\ =\ -9x^2$

c)

$y\ =\ -\frac{1}{9}x^2$

d)

$y\ =\ \frac{1}{9}x^2$

15.

What is the vertex of the transformed function (in red)?

a)

(0, -9)

b)

(-9, 0)

c)

(0, 0)

d)

(9, -9)

16.

How has the new function (in red) transformed from the parent function?

(select all that apply)

a)

reflected

b)

stretched/compressed

c)

shifted left/right

d)

shifted up/down

17.

What is the equation of the transformed function (in red)?

a)

$y\ =\ x^2\ +\ 2$

b)

$y\ =\ \left(x-1\right)^2\ +\ 2$

c)

$y\ =\ \left(x+1\right)^2\ +\ 2$

d)

$y\ =\ \left(x+2\right)^2\ +\ 1$

18.

What is the vertex of the transformed function (in red)?

a)

(2, 1)

b)

(1, 2)

c)

(1, 1)

d)

(-1, 2)

19.

How has the new function (in red) transformed from the parent function?

(select all that apply)

a)

reflected

b)

stretched/compressed

c)

shifted left/right

d)

shifted up/down

20.

What is the equation of the transformed function (in red)?

(it was stretched by a factor of 8)

a)

$y\ =\ -8x^2\ -\ 3$

b)

$y\ =\ \left(x-8\right)^2\ +\ 3$

c)

$y\ =\ -\left(x+8\right)^2\ +\ 3$

d)

$y\ =\ -\left(x+3\right)^2\ -8$

21.

What is the vertex of the transformed function (in red)?

a)

(8, 3)

b)

(0, 8)

c)

(-3, 0)

d)

(0, -3)

22.

Choose the graph of the following equation:

$y\ =\ \frac{1}{10}\left(x-4\right)^2\ -\ 3$

a)

b)

c)

23.

Choose the graph of the following equation:

$y\ =\ -6\left(x+5\right)^2\$

a)

b)

c)

24.

Choose the graph of the following equation:

$y\ =\ 12\left(x+9\right)^2\ \ +\ 6$

a)

b)

c)

25.

Choose the graph with the vertex:

(4, -3)

a)

b)

c)

26.

Choose the graph with the vertex:

(-9, 6)

a)

b)

c)

27.

Choose the graph with the vertex:

(-5, 0)

a)

b)

c)

28.

Which transformation maps the graph of

f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a reflection across the x-axis

b)

4 units up

c)

4 units to the left

d)

4 units to the right

29.

If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

30.

How did we transform from the parent function?

y = x² + 2

a)

horizontal shift up 2

b)

vertical shift up 2

c)

horizontal shift down 2

d)

vertical shift down 2

31.

How did we transform from y=x²?

y = -3x²

a)

reflection over x-axis and vertical shift down 3

b)

reflection over x-axis and vertical stretch by 3

c)

vertical stretch by -3

d)

reflection over x-axis and vertical shrink by -3

32.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

33.

What transformations have occurred?

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

34.

Compare the function y = 0.3x² to the parent function y = x²

a)

Vertical Compression by 0.3

b)

Vertical Stretch by 0.3

35.

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

a)

becoming wider or vertically compressed

b)

becoming narrower or vertically stretched

36.

Given f(x) = -x² , how did we transform from the parent function?

a)

Horizontal shift left

b)

Reflection over the x-axis

c)

Vertical shift down

d)

Vertical compression

37.

Compare the function y = 5x² to the parent function y = x²

a)

Wider

b)

Narrower

38.

Match the description to its equation.
Reflected over the x-axis
Stretched by a factor of 2

a)

A

b)

B

c)

C

d)

D

39.

How is the graph of y = x² different from the graph of
y = 1/3x²?

a)

The graph of
y = 1/3x² is shifted up.

b)

The graph of
y = 1/3x² is shifted down.

c)

The graph of
y = 1/3x² is wider.

d)

The graph of
y = 1/3x² is narrower.

40.

Given f(x) = ax² , if a > 1 , the graph will transform by

a)

becoming wider or vertically compressed

b)

becoming narrower or vertically stretched

41.

Given f(x) = -x² , what transformation does the negative make?

a)

Horizontal shift left

b)

Reflection over the x-axis

c)

Vertical shift down

d)

Vertical compression

42.

Find the equation of the parabola that has...

stretched by factor of 3

a)

y=3x^2

b)

$y=\frac{1}{3}x^2$

c)

$y=\left(x+3\right)^2$

d)

$y=x^2+3$

43.

Find the equation of the parabola that has been...

reflected

a)

y=-x^2

b)

$y=\left(x-1\right)^2$

c)

$-y=x^2$

d)

$y=x^2-1$

44.

Find the equation of the parabola that has...

been reflected

stretched by 5

a)

$y=-5x^2$

b)

$y=-\frac{1}{5}x^2$

c)

$-y=5x^2$

d)

$-y=\frac{1}{5}x^2$

45.

Which equation will cause the graph to become wider?

a)

$y=\frac{1}{8}x^2$

b)

$y=3x^2$

c)

$y=x^2-7$

d)

$y=\left(x-9\right)^2$

46.

Which equation will cause the parabola to become narrower?

a)

$y=2x^2$

b)

$y=\frac{1}{2}x^2$

c)

$y=x^2+10$

d)

$y=\left(x-6\right)^{ }$

47.

Which equation will cause the parabola to reflect and become wider?

a)

$y=-\frac{4}{5}x^2$

b)

$y=\frac{2}{3}x^2$

c)

$y=-8x^2$

d)

$y=3x^2$

48.

Convert $y=3x^2-36x$ to Vertex Form

a)

$y=3\left(x+6\right)^2-108$

b)

$y=\left(x+3\right)^2-36$

c)

$y=3\left(x-6\right)^2-108$

d)

$y=\left(x-3\right)^2+36$

49.

Which function is equivalent to $y=x^2-6x+10$ ?

a)

$y=\left(x+3\right)^2-1$

b)

$y=\left(x-3\right)^2+1$

c)

$y=\left(x+6\right)^2-10$

d)

$y=\left(x-6\right)^2+10$

50.

Which function is equivalent to $h\left(t\right)=-16t^2+32t+4$ ?

a)

$h\left(t\right)=-16\left(t-1\right)^2+3$

b)

$h\left(t\right)=-16\left(t-1\right)^2-3$

c)

$h\left(t\right)=-16\left(t-1\right)^2+20$

d)

$h\left(t\right)=-16\left(t-1\right)^2-20$

51.

The equation $2x^2-5x=-12$ is rewritten in the form $2\left(x-p\right)^2+q=0$ . What is the value of q?

a)

$\frac{167}{16}$

b)

$\frac{71}{8}$

c)

$\frac{25}{8}$

d)

$\frac{25}{16}$

52.

Which equation is equivalent to $x^2-10x=28$ ?

a)

$\left(x+10\right)^2=53$

b)

$\left(x-10\right)^2=53$

c)

$\left(x+5\right)^2=53$

d)

$\left(x-5\right)^2=53$

53.

Which choice gives a different form of $g\left(x\right)=x^2+6x+10$ and also the axis of symmetry?

a)

$g'\left(x\right)=\left(x-3\right)^2=1;\ x=-3$

b)

$g'\left(x\right)=\left(x+3\right)^2=1;\ x=3$

c)

$g'\left(x\right)=\left(x-3\right)^2=-1;\ x=3$

d)

$g'\left(x\right)=\left(x+3\right)^2=-1;\ x=-3$

54.

Find the quadratic regression equation for the relationship of the horizontal distance and the height of the ball in the provided table.

a)

$-18x^2+2.11x+4.21$

b)

$-0.06x^2+1.06x+7.9$

c)

$-6x^2+1.06x+79$

d)

$-0.12x^2+2.11x+4.22$

55.

Find the height of the ball when it traveled a distance of 10 feet.

a)

12.8 ft

b)

13.5 ft

c)

11.1 ft

d)

17 ft

56.

Find the best fitting quadratic model for the data given.

a)

$1.2x^2+13x+504.3$

b)

$12x^2+13x+504.3$

c)

$0.12x^2+1.3x+504.3$

57.

Find the population for 1975.

HINT: Read the headers on the table!

a)

623 thousand people

b)

650 thousand people

c)

599 thousand people

d)

513 thousand people

58.

Use the given points to find the equation of the line of best fit (regression equation).

Enter your answer as y=ax^2+bx+c

(a)

59.

The table shows the population of a town from 1996 to 2004. Assume that t is the number of years since 1996 and P is measured in thousands of people.
Which of the following is the model that best fits the data rounded to the nearest tenth?

a)

$P\left(t\right)=-0.21x^2+2.08x+22.96$

b)

$P\left(t\right)=-.2x^2+2x+22.9$

c)

$P\left(t\right)=-.2x^2+2.1x+23.0$

d)

$P\left(t\right)=-.2x^2+2.1x+22.9$

60.

"Use the results of the regression shown to predict the population in 2007. "

What value of x will you be plugging into your equation??

(a)

61.

Using the regression equation rounded to TWO decimal places, what would be the estimated population for the year 2007?

*Your answer should be a whole number in the thousands!

(a)

62.

Name the x-intercept(s)?

a)

(0, 0)

b)

(2, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

63.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

64.

Is this point a max or min?

a)

max

b)

min

65.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

66.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

67.

Determine key features from the give function.

g\left(x\right)=\left(x-3\right)^2-16

a)

Positive function with a minimum

b)

Negative function with a maximum

c)

Vertex located at (3, -16), and an axis of symmetry at x = 3

d)

Vertex located at (3, -16) and an axis of symmetry at y = -16

e)

Reflects over the x-axis

68.

Determine the x-intercepts of the given function by solving for x.

g\left(x\right)=\left(x-3\right)^2-16

a)

x-intercepts are located at (7, 0) and (-1, 0)

b)

x-intercepts are located at (19, 0) and (13, 0)

c)

x-intercepts are located at (11, 0) and (-5, 0)

d)

x-intercepts are located at (1, 0) and (-7, 0)

69.

Convert the given function to standard form and locate the y-intercept.

h\left(x\right)=-4\left(x+2\right)^2+100

a)

$h\left(x\right)=-4x^2-16x+116$

The y-intercept is (0, 116)

b)

$g\left(x\right)=-4x^2-16x-104$

The y-intercept is (0, -104)

c)

$g\left(x\right)=-4x^2+4x+104$

The y-intercept is (0, 104)

d)

$g\left(x\right)=-4x^2-16x+84$

The y-intercept is (0, 84)

Lopez Unit 2B Review

Total questions: 69

Worksheet time: 4hrs 11mins

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