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WorksheetsChapter 2 Quadratic Functions
Total questions: 40
Worksheet time: 2hrs 4mins
Name
Class
Date
1.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
2.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
3.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
4.
What is the equation for this parabola in factored form?
a)
y=(x+2)(x-1)
b)
y=(x-2)(x+1)
c)
y=(x-2)(x-1)
d)
y=(x+2)(x+1)
5.
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
6.
The vertex of this parabola is...
a)
(-4, -12.5)
b)
(12.5, 4)
c)
(-12.5, -4)
d)
(4, 12.5)
7.
A parabola is upside-down when a is:
a)
negative
b)
positive
c)
0
d)
infinite
8.
Which answer choice describes y = -3x2 +7x - 2 accurately?
a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum
9.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
10.
If the discriminant equals 0, then the quadratic has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
11.
Simplify the following radical: √-243
a)
81√3
b)
3√3
c)
13√3
d)
9i√3
12.
How many solutions are there if the discriminant is positive.
a)
0
b)
1
c)
2
d)
Infinite
13.
What is the vertex of the quadratic function:
y = x2 - 6x + 11?
y = x2 - 6x + 11?
a)
(3,2)
b)
(-3,-2)
c)
(-3,2)
d)
(3,-2)
14.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
15.
Identify the vertex and whether the graph opens up or down.
a)
(-1, 4); opens up
b)
(-1, 4); opens down
c)
(1, 4); opens up
d)
(1, 4); opens down
16.
a)
-2, 4
b)
-8
c)
±8
d)
No real solution
17.
Solve
6x2 + 17x + 12 = 0
6x2 + 17x + 12 = 0
a)
x = -4/3, x = -3/2
b)
x = 9, x = 8
c)
x = 4, x = 3
d)
x = -4, x = -3
18.
Solve
5x2 - 28x + 32 = 0
5x2 - 28x + 32 = 0
a)
x = 10/3, x = -6
b)
x = 8, x = 4/5
c)
x = 8/5, x = 4
d)
x = 8/5, x = -7
19.
Solve
3x² + 5x - 12 = 0
3x² + 5x - 12 = 0
a)
x = -4/3, x = 3
b)
x = 4/3, x = -3
c)
x = -1, x = 4
d)
x = 1, x = -4
20.
To solve by completing the square, what needs to be moved in this equation?
x2 = 9 - 4x
x2 = 9 - 4x
a)
the -4x
b)
the 9
c)
the x2
21.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
22.
Solve by completing the square:
k2 − 12k + 23 = 0
k2 − 12k + 23 = 0
a)
{6 + √13, 6 - √13}
b)
{-6 + √13, -6 - √13}
c)
{6 + √59, 6 - √59}
d)
{-6 + √59, -6 - √59}
23.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
24.
Find the difference.
(6 - 8i) - (1 - 3i)
(6 - 8i) - (1 - 3i)
a)
9 + 5i
b)
5 - 11i
c)
5 - 5i
d)
7 + 5i
25.
(3+8i)(-2-i)
a)
2-19i
b)
23-i
c)
34+5i
d)
23-i
26.
i79
a)
i
b)
1
c)
-1
d)
-i
27.
Simplify:
(-3i)(4i)(-5i)
(-3i)(4i)(-5i)
a)
-60i
b)
60
c)
-60
d)
60i
28.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
29.
If the graph of a quadratic does not intercept the x-axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
30.
Convert to vertex form.
a)
y=3(x+1)2 - 8
b)
y=3(x-1) 2 - 8
c)
y=3(x+2)2 - 8
d)
y=3(x-2)2 - 8
31.
What is the equation for the axis of symmetry of
f(x)= (x +1)2 + 5
f(x)= (x +1)2 + 5
a)
x = 1
b)
x = -1
c)
x = -5
d)
x = 5
32.
How did we transform from the parent function?
g(x) = -1/5(x - 1)2 + 7
g(x) = -1/5(x - 1)2 + 7
a)
reflection, vertical compression, horizontal right, vertical up
b)
vertical compression, horizontal shift left, vertical shift up
c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
33.
What is the significance of the ordered pair (0, -1.5) to the graph?
a)
It is the maximum point
b)
It is the vertex
c)
It is the y-intercept
d)
It is an x-intercept
34.
What are the solutions of 7x2 + 8x + 1 = 0? Solve using the quadratic formula.
a)
-1, 1/7
b)
1, 7
c)
-1, -7
d)
-1, -1/7
35.
Solve using the Quadratic Formula:
2x2 + x - 4 = 0
a)
x = -¼ and x = -2
b)
x = 1.19 and x = -1.69
c)
x = 8 and x = -4
d)
x = 1.69 and x = 1.20
36.
Solve x2 - 5x + 10 = 0
a)
(5 - i√15)/2 , (5 + i√15)/2
b)
(5 - √15)/2 , (5 + √15)/2
c)
(5 - i√65)/2 , (5 + i√65)/2
d)
(5 - √65)/2 , (5 + √65)/2
37.
Determine the values of
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
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
38.
Solve
(x+3)2-5 = 9
(x+3)2-5 = 9
a)
-3±√14
b)
3±√14
c)
±11
d)
±5
39.
The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 40t + 2. From what height was the balloon released?
a)
2 meters
b)
5 meters
c)
40 meters
d)
20 meters
40.
A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t2 + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?
How many seconds will it take the ball to hit the ground?
a)
126.56 ft
b)
5.625 sec
c)
2.81 sec
d)
0 ft
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