WorksheetsCompleting the Square
Total questions: 10
Worksheet time: 50mins
Name
Class
Date
1.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
2.
What is the first step to solving THIS equation by completing the square?
a2 + 10a + 21 = 0
a2 + 10a + 21 = 0
a)
Set the equation equal to zero
b)
Divide 10 by 2 and add the result to both sides
c)
Add a2 and 10a together
d)
Subtract the 21
3.
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
4.
Complete the square.
x2 + 6x + ____
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
5.
Convert to vertex form:
y = x2 + 4x + 10
a)
y = (x + 4)2 + 6
b)
y = (x + 2)2 + 6
c)
y = (x + 4)2 - 6
d)
y = (x + 2)2 - 6
6.
In vertex form,
f(x) = a(x - h)2 + k
what does the h stand for?
a)
the y-coordinate of the vertex
b)
the x-coordinate of the vertex
c)
the x-intercept
d)
the y-intercept
7.
x2+8x+c=20+c
Rewrite the above equation into a perfect square binomial form.
(𝑥 +_______) 2 = ________
a)
(x−4)2=4
b)
(x+4)2=36
c)
(x−8)2=12
d)
(x+8)2=28
8.
If given the equation y = 3(x + 5)2 - 4, what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
9.
Solve by completing the square.
x2 +12x = 5
x2 +12x = 5
a)
X = 6 + √41 or 6 − √41
b)
X= 35 or 47
c)
X = −6 + √41 or −6 − √41
d)
X = √35 or √47
10.
What is one of the solutions to this equation?
(x - 3)2 = 49
a)
7
b)
-7
c)
-4
d)
4
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