Free Printable Quadratic Relations Review

1.

Which of the following is the standard form of a quadratic equation?

a)

$ax^2 + bx + c = 0$

b)

$ax + b = 0$

c)

$ax^3 + bx^2 + cx + d = 0$

d)

$a(x - h)^2 + k = 0$

2.

What is the vertex form of a quadratic equation?

a)

$y = ax^2 + bx + c$

b)

$y = a(x - h)^2 + k$

c)

$y = ax + b$

d)

$y = a(x - p)(x - q)$

3.

Which of the following is a characteristic of the graph of a quadratic function?

a)

It is a straight line.

b)

It is a parabola.

c)

It is a circle.

d)

It is a hyperbola.

4.

If a quadratic function opens upwards, what can be said about the leading coefficient $a$ ?

a)

$a > 0$

b)

$a < 0$

c)

$a = 0$

d)

$a \leq 0$

5.

Which graph represents a quadratic relation?

a)

b)

c)

d)

6.

Which of the following equations represents a quadratic relation?

a)

$y=3x+1$

b)

$2x+y\ =3$

c)

$y=2x^3$

d)

$y=2x^2+1$

7.

Which finite difference is constant for a quadratic equation?

a)

First

b)

Second

c)

Third

d)

No Pattern

8.

What type of function does this table represent?

a)

Linear

b)

Quadratic

c)

Cubic

d)

Exponential

9.

What type of function is represented by the following table?

a)

Exponential

b)

Quadratic

c)

Cubic

d)

Linear

10.

What is the first finite difference in the table shown?

a)

0.5

b)

0

c)

-1.25

d)

0.25

11.

Which finite difference is constant for a linear relation?

a)

The second finite difference

b)

None of the finite differences

c)

The first finite difference

d)

The third finite difference

12.

If you use a difference table and find that the first differences are not constant and the second differences are not constant, this must mean......

a)

That this is a linear relation

b)

That this is a quadratic relation

c)

That this is neither a linear or a quadratic relation

d)

That you have made a mistake

13.

The function f(x) = x²+ 8x - 2

a)

Vertex form

b)

original form

c)

integer form

d)

standard form

14.

The coordinates of the vertex in this function f(x)= 3 (x+1)² +4

a)

(1,4)

b)

(3,4)

c)

(-1,4)

d)

(3,1)

15.

The coordinates of the y-intercept in this function f(x) = x²+ 8x - 2

a)

(0,0)

b)

(2,0)

c)

(0,-2)

d)

(-2,0)

16.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

17.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

18.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

19.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

20.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

21.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

22.

Which point is an example of a y-intercept?

a)

(3,4)

b)

(-2,8)

c)

(0,4)

d)

(5,0)

23.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

24.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

25.

Which quadratic equation models the parabola shown?

a)

y = (x-2)(x+5)

b)

y = (x+2)(x+5)

c)

y = -(x-2)(x-5)

d)

y = -(x+2)(x+5)

26.

Which quadratic equation models the parabola shown below?

a)

y = 0.25(x-2)(x+2)

b)

y = -0.25(x-2)(x+2)

c)

y = 4(x-2)(x+2)

27.

Which of the following is the Factored Form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = ax² + bx + c

c)

f(x) = a(x - m)(x - n)

d)

f(x) = a(x - h)² + k

28.

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

a)

(-2, 0) and (6, 0)

b)

(2, 0) and (-6, 0)

c)

(-2, 6)

d)

(¼, 0) and (-2, 0) and (6, 0)

29.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

30.

In f(x) = a(x - p)(x - q), what does "a" tell us?

a)

The slope

b)

If the Parabola opens up or down

c)

x coordinate of the x - intercept

d)

y coordinate of the y - intercept

31.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

32.

What equation represents the quadratic function?

a)

y = (x - 5)² - 3

b)

y = (x - 5)² + 3

c)

y = (x + 5)² - 3

d)

y = (x - 3)² - 5

33.

What equation represents the quadratic function?

a)

y = (x - 7)² - 2

b)

y = (x + 7)² + 2

c)

y = (x + 7)² - 2

d)

y = (x + 2)² + 7

34.

What equation represents the quadratic function?

a)

y = -(x - 5)²

b)

y = -x² + 5

c)

y = x² - 5

d)

y = (x - 5)²

35.

What equation represents the quadratic function?

a)

y = -(x - 6)² - 3

b)

y = -(x - 6)² + 3

c)

y = -(x + 6)² - 3

d)

y = -(x + 6)² + 3

36.

What equation represents the quadratic function?

a)

y = (x - 4)² + 1

b)

y = (x + 1)² - 4

c)

y = (x - 4)² - 1

d)

y = (x - 1)² - 4

37.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

38.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

39.

What steps transform the graph y = x² to y = (x-4)²

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

40.

Does the parabola
f(x)=4(x-2)² + 3
open up or down?

a)

up

b)

down

41.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

42.

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

a)

g(x)=f(x + 3)

b)

g(x)=f(x - 3)

c)

g(x)=f(x) + 3

d)

g(x)=f(x) - 2

43.

How did we transform from y=x^2?

y = -3x²

a)

vertical reflection and vertical shift down

b)

vertical reflection and vertical stretch

c)

horizontal stretch

d)

vertical reflection and vertical compression

44.

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

a)

Shifts the function left or right

b)

Reflects over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

45.

In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?

a)

Shifts the function left or right

b)

Reflection over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

46.

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

47.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

48.

On the May 24th weekend, the The City of Hamilton sets off fireworks at Bayfront Park.
The path of a particular firework rocket is modeled by the relation
$h=-4.2\left(t-3\right)^2+40$

where h is the rocket’s height above the water, in metres, and t is the time, in seconds.
What is the maximum height of the rocket?

a)

4.2 metres

b)

3 metres

c)

40 metres

d)

100 metres

49.

On the May 24th weekend, the The City of Hamilton sets off fireworks at Bayfront Park. The path of a particular firework rocket is modeled by the relation
$h=-4.2\left(t-3\right)^2+40$

where h is the rocket’s height above the water, in metres, and t is the time, in seconds.
Determine the height of the rocket after 2 seconds.

a)

40 metres

b)

100 metres

c)

35.8 metres

d)

5 metres

50.

A rider on a mountain bike jumps off a ledge. His path is modeled by the relation

h = -0.9d² + 0.9d + 5.4

In factored form: h = -0.9(d – 3)(d + 2)

Where h is his height above the ground and d is his horizontal distance from the ledge, both in meters.

How far was the rider from the ledge when he landed?

a)

0 metres

b)

1 metre

c)

2 metres

d)

3 metres

51.

In a table of values, if the "first differences" are all equal, this tells us that the relation must be:

(a)

52.

In a table of values, if the "second differences" are all equal, but not zero, this tells us that the relation must be:

(a)

53.

If you graph the quadratic relation $y=-5x^2+8x-3$ , the constant term in the equation (-3) represents the:

a)

x-intercept

b)

y-intercept

c)

vertex

d)

vertical shift

54.

This vertical line can be drawn through the centre of a parabola and cuts the parabola directly in half.

a)

Axis of symmetry

b)

Vertex line

c)

y-axis

d)

Asymptote

55.

The parabola represented by the equation $y=-x^2+4x-3$ :

a)

Opens up

b)

Opens down

c)

Opens left

d)

Opens right

56.

Compared to the parabola $y=x^2$ , which parabola is vertically stretched (narrow)?

a)

$y=\frac{1}{2}x^2+4$

b)

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

c)

$y=x^2+8x$

d)

$y=3x^2-x+1$

57.

Compared to the parabola $y=x^2$ , which parabola is vertically compressed (wide)?

a)

$y=\frac{1}{2}x^2+4$

b)

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

c)

$y=x^2+8x$

d)

$y=3x^2-x+1$

58.

Compared to the parabola $y=x^2$ , which parabola is reflected in the x-axis (opens down)?

a)

$y=\frac{1}{2}x^2+4$

b)

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

c)

$y=x^2+8x$

d)

$y=3x^2-x+1$

59.

Which equation best represents the parabola shown on the graph?

a)

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

b)

$y=x^2+4$

c)

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

d)

$y=x^2-4$

60.

Which equation best represents the parabola shown on the graph?

a)

$y=\left(x-5\right)^2-1$

b)

$y=\left(x-1\right)^2-5$

c)

$y=\left(x-5\right)^2+1$

d)

$y=\left(x+1\right)^2-5$

61.

Which equation best represents the parabola shown on the graph?

a)

$y=-x^2-2$

b)

$y=-2x^2$

c)

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

d)

$y=x^2-2$

62.

Which equation best represents the parabola shown on the graph?

a)

$y=x^2+1$

b)

$y=-x^2-1$

c)

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

d)

$y=x^2-1$

63.

Compared to the graph of $y=x^2$ , which parabola is:

reflected in the x-axis AND vertically stretched by a factor of 2 AND shifted 1 unit down?

a)

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

b)

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

c)

$y=-2x^2-1$

d)

$y=-x^2-2$

64.

Standard form of a quadratic equation

a)

y=x²

b)

y=ax²+bx+c

c)

y=mx+b

d)

y=x

65.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

66.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

67.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

68.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

69.

This equation is in f(x)= 3 (x+1)² +4

a)

original form

b)

vertex form

c)

standard form

d)

quadratic form

70.

The coordinates of the vertex in this function f(x)= 3 (x+1)² +4

a)

(1,4)

b)

(3,4)

c)

(-1,4)

d)

(3,1)

71.

The coordinates of the y-intercept in this function f(x) = x²+ 8x - 2

a)

(0,0)

b)

(2,0)

c)

(0,-2)

d)

(-2,0)

72.

A parabola is upside-down when a is:

a)

negative

b)

positive

c)

0

d)

infinite

73.

What is the axis of symmetry for the following equation?

y=4x²-8x+9

a)

x = 5

b)

x=1

c)

y = 1

d)

y = 5

74.

What is the vertex of the quadratic function: y=1/2(x-3)²+8?

a)

(3,8)

b)

(-3,-8)

c)

(-3,8)

d)

(3,-8)

75.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

Quadratic Relations Review

Total questions: 75

Worksheet time: 12hrs 39mins

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