Solving Quadratic Equations Worksheet By Using The Quadratic Formula With Answers Page 9
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109-5 Solving Quadratic Equations by Using the Quadratic Formula
The solutions are 1.6 or 7.4.
The value of x is 58 or 64.
2
Describe the transformations needed to obtain
62. What are the solutions of the quadratic equation 6h
the graph of g(x) from the graph of f (x).
+ 6h = 72?
2
A 3 or −4
66. f (x) = 4x
2
B −3 or 4
g(x) = 2x
C no solution
SOLUTION:
D 12 or −48
2
The graph of g(x) = ax
stretches or compresses the
SOLUTION:
2
graph of f (x) = 4x
vertically. The change in a is
,
Write the equation in standard form.
2
and 0 <
< 1. If 0 <
< 1, the graph of f (x) = x
For this equation, a = 6, b = 6, and c = –72.
is compressed vertically. Therefore, the graph of y =
2
2
2x
is the graph of y = 4x
vertically compressed.
2
68. f (x) = x
− 6
2
g(x) = x
+ 3
SOLUTION:
2
The graph of f (x) = x
+ c represents a vertical
translation of the parent graph. The value of the
change in c is 9, and 9 > 0. If c > 0, the graph of f (x)
2
units up. Therefore, the graph of
= x
is translated
2
2
y = x
+3 is a translation of the graph of y = x
–6
shifted up 9 units.
Determine whether each graph shows a positive
The solutions are –4 or 3.
correlation, a negative correlation, or no
So, the correct choicer is A.
correlation. If there is a positive or negative
correlation, describe its meaning in the
Solve each equation by completing the square.
situation.
Round to the nearest tenth if necessary.
2
64. x
− 9x = −12
SOLUTION:
70.
The solutions are 1.6 or 7.4.
SOLUTION:
The graph shows no correlation between the year
Describe the transformations needed to obtain
and the number of hurricanes because the points are
the graph of g (x) from the graph of f (x).
randomly spread out.
2
66. f (x) = 4x
2
g(x) = 2x
Determine whether each sequence is
SOLUTION:
arithmetic, geometric, or neither. Explain.
72. 20, 25, 30, ...
2
The graph of g(x) = ax
stretches or compresses the
SOLUTION:
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Page 9
2
graph of f (x) = 4x
vertically. The change in a is
,
Check the difference and ratio between terms.
2
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