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Problem R.8
CONCEPT PREVIEW Use choices A–D to answer each question.
A. 3x² - 17x - 6 = 0
B.(2x + 5)² = 7
C. x² + x = 12
D. (3x - 1) (x - 7) = 0
Which quadratic equation is set up for direct use of the square root property? Solve it.
Problem R.42
Solve each quadratic equation using the zero-factor property. See Example 5.
x² + 2x - 8 = 0
Problem 1
Fill in the blank(s) to correctly complete each sentence.
To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.
Problem 1.1
Fill in the blank(s) to correctly complete each sentence.
The sum of the measures of the angles of any triangle is ________________ .
Problem 1.15
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel.
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Problem 1.3
Fill in the blank(s) to correctly complete each sentence.
An equilateral triangle has _________________ equal sides.
Problem 2
Fill in the blank(s) to correctly complete each sentence.
An isosceles right triangle has one ________________ angle and ______________ equal sides.
Problem 3
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.
Problem 5
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.
Problem 6
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the ___-axis.
Problem 11
Work each matching problem.
Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x².
I II
a. y = (x - 7)² A. a translation to the left 7 units
b. y = x² - 7 B. a translation to the right 7 units
c. y = 7x² C. a translation up 7 units
d. y = (x + 7)² D. a translation down 7 units
e. y = x² + 7 E. a vertical stretching by a factor of 7
Problem 13
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
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Problem 50
Solve each quadratic equation using the zero-factor property. See Example 5.
9x² - 12x + 4 = 0
Problem 67
Solve each quadratic equation using the quadratic formula. See Example 7.
x² - x - 1 = 0
Problem 70
Solve each quadratic equation using the quadratic formula. See Example 7.
-3x² + 6x + 5 = 0