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WorksheetsCubics review
Total questions: 28
Worksheet time: 3hrs 59mins
Name
Class
Date
1.
Find p(-2) for p(x) = 4x3+3x2-x+5
a)
51
b)
-17
c)
-13
d)
-37
2.
Divide x3 + x2 - 14x - 24 by x+2
a)
x2-x-12
b)
x2+x+12
c)
x2-x-16
d)
2x2-x-12
3.
If x3-7x2+5x-4 = (x-3)(x2+bx+c)+r
Find b, c and r.
Find b, c and r.
a)
b= -11, c= -7, r= -25
b)
b= -4, c= 17, r= -25
c)
b= -4, c= -7, r= -17
d)
b= -4, c= -7, r= -25
4.
Find the remainder when x3+3x2+2x+1 is divided by x-2
a)
x2+5x+12
b)
-23
c)
25
d)
-25
5.
Fully factorise x3-2x2-5x+6
a)
(x-1)(x-3)(x+2)
b)
(x-1)(x+3)(x+2)
c)
(x+1)(x-3)(x-2)
d)
(x-1)(x-6)(x+1)
6.
Where is the point of inflection?
f(x)=(x+15)3-10
a)
(-10, 15)
b)
(15, -10)
c)
(-15,10)
d)
(-15,-10)
7.
Which parent function matches the graph?
a)
y = |x|
b)
y = ∛(x)
c)
y = x2
d)
y = a⋅bx
8.
All of the y values or outputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
9.
Where is the point of inflection?
f(x)= -2(x-3)3+1
a)
(3,1)
b)
(-3,1)
c)
(-2,3)
d)
(3,-2)
10.
Find all zeros for the polynomial function P(x) = x3 -3x2-5x+15
a)
3, √5
b)
3, √5, -√5
c)
-3, √5, -√5
d)
-3, 5i, -5i
11.
Find all zeros of the polynomial function P(x) = x3+6x2+9x+54
a)
6, 3, -3
b)
-6, 3, -3
c)
-6, 3i, -3i
d)
6, 3i, -3i
12.
Solve the following equation:
x4 + x2 - 90 = 0
x4 + x2 - 90 = 0
a)
3, -3, ±√10
b)
3, -3
c)
±√10
d)
3
13.
Solve the following equation:
x4 - 6x2 + 8 = 0
x4 - 6x2 + 8 = 0
a)
2, -2
b)
2, -2, √2, 2i
c)
√2, -√2
d)
2, -2, √2, -√2
14.
Solve the following equation:
x4 + x2 - 90 = 0
a)
3, -3, ±√10
b)
3, -3
c)
±√10
d)
3
15.
1. X4 - 7X2 + 12 = 0
a)
A) {0, 4, -4, 4}
b)
b) { 3, -3, -2, 2"
c)
c){ √3, -√3 , 2, -2 }
d)
D) { ±3, ±2 }
16.
What is the equation of the graph shown?
a)
y= (x-2)3 + 4
b)
y= (x+2)3 + 4
c)
y = - (x-2)3 + 4
d)
y= - (x+2)3 + 4
17.
Determine the roots of the polynomial.
f(x) = x(x+5)(x - 8)
f(x) = x(x+5)(x - 8)
a)
0, -5
b)
0, 8, 5
c)
0, -5, 8
d)
-8, 0, 5
18.
Determine the roots of the polynomial.
f(x) = x(x+4)(x-2)
f(x) = x(x+4)(x-2)
a)
0, -4, 2
b)
-6, -4, 2
c)
-6, 4, -2
d)
0, 4, -2
19.
Which equation below is a cubic function translated left 4 units?
a)
y = x3 + 4
b)
y = (x + 4)3
c)
y = (x - 4)3
d)
y = 4x3
20.
Which equation represents a parent function y = x3 translated 4 units to the right and 1 unit up?
a)
y = (x + 4)3 + 1
b)
y = (x - 4)3 + 1
c)
y = (x + 1)3 + 4
d)
y = (x - 1)3 + 4
21.
WHAT IS THE RANGE OF EVERY SINGLE CUBIC FUNCTION expressed in interval notation!?
a)
(-∞,∞)
b)
[0,∞)
c)
-∞<y<∞
d)
[-∞,∞]
22.
WHAT IS THE DOMAIN OF EVERY SINGLE CUBIC FUNCTION!?
a)
(-∞,∞)
b)
[0,∞)
c)
(-∞,0]
d)
[-∞,∞]
23.
How did we transform from the parent function Y = X3?
y = -1/5(x - 1)3 + 7
y = -1/5(x - 1)3 + 7
a)
reflection across the x-axis, vertical compression, horizontal shift to the right 1, vertical shift 7 up
b)
vertical compression, horizontal shift left 1, vertical shift up 7
c)
reflection, horizontal shift 1 right, vertical shift 7 down
d)
no changes were made to y = x2
24.
What is another way to say "where a function crosses the x-axis"?
a)
x-intercept
b)
zero
c)
root
d)
all of these.
25.
Determine the roots of the polynomial.
f(x) = (x+1)(x-4)(x+2)
f(x) = (x+1)(x-4)(x+2)
a)
1, 4, 2
b)
-1, -4, -2
c)
1, -4, 2
d)
-1, 4, -2
26.
Where is the point of inflection for f(x)= x3?
a)
no vertex
b)
(1,1)
c)
(0,0)
d)
(3,0)
27.
Factor x3-125
a)
(x-5)(x2+5x+25)
b)
(x+5)(x2-5x+25)
c)
(x-5)(x2+5x+5)
d)
(x+5)(x2-5x+5)
28.
Factor 8x3+216
a)
(2x+6)(4x2-12x+36)
b)
(2x-6)(4x2+12x+36)
c)
(4x+6)(16x2-24x+36)
d)
(4x-6)(16x2+24x+36)
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