248 terms

# Algebra Chapter 1-9 Review

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Write a verbal expression for 6x + 7
Six times x plus seven
Write a verbal expression for the algebraic expression 5(x² +2)
Five times the quantity x squared plus two
Write an algebraic expression for the product of ten and x
10x
Write an algebraic expression for the sum of eight and the square of a number x
8 + x²
Evaluate the expression 5 raised to the fourth
625
Evaluate 162 ÷ [6(7 − 4)²]
3
Evaluate 6²+ 3 ∙ 7 − 9
48
Evaluate 30 − 5 ∙ 4 + 2
12
Evaluate if a = 12, b = 9, c = 4 a² + b − c²
137
Evaluate and name the property used in each step 2 + 6(9− 3²) − 2
2 + 6 (9 − 9) − 2 (sub) . . . . . . . . . . . . . . . . . . . . 2 + 6(0) − 2 (sub) . . . . . . . . . . . . . . . . . . . . . . . . 2 + 0 − 2 (Mult prop of zero). . . . . .. . .. . . . .. . 2-2 (add iden). . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 (sub) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Find the value for n and name the property 5 · n · 2 = 0
n = 0 multiplication property of zero
Find the value for n and name the property used: 11· n = 11
n = 1 Multiplicative identity
Find the value for n and name the property used: 7 + n = 7
Find the value of n and name the property used: 3 · 1/3 = n
n = 1 Multiplicative inverse or reciprocal
Evaluate if x = 2, y = 3, z = 4 2xyz + 5
53
Simplify the expression. If not possible, write simplified 3x + 6x
9x
Simplify the expression. If not possible, write simplified 5x + 4 + 3x² − 3x
3x² + 2x + 4
Simplify the expression. If not possible write simplified 3x + 2(4y + 5x)
13x + 8y
Simplify the expression. If not possible write simplified 7(2x + 5)
14x + 35
Find the solution set if the replacement set is x = {4, 5, 6, 7, 8} for the equation 5x − 9 = 26
7
Find the solution set if the replacement set is x = {0. 1/2, 1, 3/2, 2} for the equation 120 − 28x = 78
3/2
Solve the equation that follows 2(x + 2) =20
8
List the domain and the range for the following relation {(−2,−1), (3, 3), (4,3)}
Domain = {−2, 3, 4} Range = {−1, 3}
Identify the hypothesis and conclusion for the following relation: If it is Sunday, then mail is not delivered
Hypothesis: It is Sunday Conclusion: mail is not delivered
Explain the difference between an algebraic expression and a verbal expression.
Algebraic expression consists of numbers, variables, and arithmetic operations. Verbal expression consists of words.
f(x) = 2x − 4 Find the value of f(−5)
−14
f(x) = 2x − 4 Find f(k + 1)
2k − 2
f(x) = x² + 3 Find f(b) + 4
b² + 7
Determine whether each pair of ratios is an equivalent ratio. 5/9, 7/11
No because when you cross multiply, 55 is not equal to 63
Solve 2/3 n + 8 = 1/3 n + 2
−18
Solve the equation. Show work. |5y − 2| = 7
−1, 9/5
Solve the equation. Show work. x/5 + 6 = 2
− 20
State whether the percent of change is a percent of increase or percent of decrease. Find the percent of change to the nearest whole percent. Original \$25, New \$10
Decrease of 60%
Two trains leave Chicago, one traveling east at 30 miles per hour and one traveling west at 40 miles per hour. When will the trains be 210 miles apart?
3 hours
Evaluate if x = −1, y = 3, and z = −4. . . . . . . . |−3y + z| − x
14
Solve the equation for the variable a listed . . . 7a − b = 15a for a
a = −b/8
Solve −2m = 16
m = −8
Solve h/3 = −2
h = − 6
Write an equation and solve. X plus 10 is equal to 3 times x.
x + 10 = 3x When the equation is solved, x = 5
Write an equation and solve. Twenty decreased by three times a number equals −10.
20 − 3x = −10 When the equation is solved, x = 10
Choc chip cookies sell for \$6.95 and white choc cookies sell for \$5.95 per lb. How many pounds of choc chip cookies must be mixed with 4 lbs of white choc cookies to obtain a mixture that sells for \$6.75 per pound
16 pounds
Dress \$69 and tax is 5 %. Find the total price
\$72.45
Backpack \$56.25. Discount 20%. Find the discounted price
\$45.00
Find three consecutive integers whose sum is 36
11, 12, 13
Find two consecutive even integers whose sum is 126.
62, 64
Find three consecutive odd integers whose sum is 117
37, 39, 41
Solve 18 − 4x = 42
x = −6
Solve −x/3 − 4 = 13
−51
Solve the equation for the variable indicated. 7x + 3y = m, for y
y = (m − 7x)/3
Solve the proportion. . . . . . . . . 9/(y + 1) = 18/54
26
Solve 5(x + 3)+9= 3(x − 2) + 6
x = −12
Solve 3(x + 1) − 5 = 3x −2
All numbers
Solve 3(x − 6) = 3x
No solution
Translate the equation in to a sentence 2x + 10 = 26
Two times x plus ten equals twenty-six or the product of two and x increased by ten is twenty-six.
Solve |x + 1| = 5
−6 and 4
Solve (4x + 7)/15 = (6x +2)/10
0.8
Solve 3.2x − 4.3 = 12.6x + 14.5
x = −2
Translate the sentence in to an equation. Three times the sum of g and h is 12.
3(g + h) = 12
Translate the sentence in to an equation. Twice a increased by the cube of a equals b
2a + a³ = b
Look at problem 17 on page 176. You will see a graph. What is the slope of the graph?
1/2
Look at problem 16 on page 176. You will see a graph. What is the slope of the graph?
−4/3
Determine whether the equation is linear or not. If yes, write the equation in standard form xy = 6
No, because variables are multiplied together
Determine whether the equation is linear or not. If yes, write the equation in standard form y = 2 − 3x
Yes. 3x + y = 2
Determine whether the equation is linear or not. If yes, write the equation in standard form y = 3x² + 1
No, because the x is raised to a power greater than one
y = 2x The constant of variation is _________
2
y = 2x The slope is ____________
2
Look at problem 11 on page 183. Name the constant of variation. What is the slope?
Constant of variation is −5 The slope is −5
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. If y = −4 when x = 2, find y when x = −6.
The equation is y = −2x. The value for y is 12
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Solve. If y = 7.5 when x = .5, find y when x = −0.3.
The equation is y = 15x. The value for y is −4.5
Solve the equation 4x − 1 = 0
x = 1/4
Find the value of r so the line that passes through each pair of points has the given slope. (r, 3), (5, 9), m = 2
r = 2
Find the value of r so the line that passes through each pair of points has the given slope. (−4, 3)), (r, 5), m= 1/4
r = 4
Graph 2x + 4y = 16 using x an y intercepts
x intercept is 8, and the y intercept is 4. See page 155 and 156 to check the work and graph
Graph y = 1/3 x + 2 using a table
Some points on the line are (0, 2),(3, 3), (6, 4). Check page 156 to see the graph.
Graph y = −6x
Some points on the line are (0, 0), (1, −6),(−1, 6) See page 181 for a picture of the graph
Find the next three terms of the arithmetic sequence 22, 20, 18, 16 ...
14, 12, 10
Find the next three terms of the arithmetic sequence 3.1, 4.1, 5.1, 6.1 ...
7.1, 8.1, 9.1
Write an equation for the nth term of the arithmetic sequence 7, 13, 19, 25 ...
The nth term = 6n + 1
Write an equation for the nth term of the arithmetic sequence 30, 26, 22, 18 ....
The nth term = −4n + 34
Look at the graph for problem #7 on page 198. Write an equation for the graph in function notation
f(x) = 3x − 2
Look at the graph for problem #3 on page 198. Write an equation for the graph in function notation
f(x) = −x + 3
What point does every direct variation equation go through?
(0, 0)
What is the general equation for a direct variation equation?
y = kx
Which of the following equations is a direct variation equation? y = x + 2 or y = 3x
y = 3x because it is of the form y = kx
Find the slope of the line that passes through (6, 1) and (−6, 1)
0
Find the slope of the line that passes through (5, 2) and (5, −2)
Undefined
Find the slope of the line that passes through (10, 0) and (−2, 4)
−1/3
Solve the equation 15x −30 = 5x − 50 by graphing and algebraically
Graph f(x) = 10x + 20 and it crosses the x-axis at − 2. Solve 10x + 20 and x = −2
Solve the equation 0 = 4 − 2x
x = 2
Graph 2x + y = −2 using the x and y intercepts
x intercept is −1 and the y intercept is −2
Graph y − x = 4 using a table
Solve the equation for y. y = x + 4. Some points on the line are (0, 4), (1, 5), (−1, 3)
Define slope
(y2 − y1)/(x2 − x1) Other definitions are rise/run and change in y/change in x
Is the following an arithmetic sequence 1, 4, 9, 16...
No. There is not a common difference.
In the equation, y = mx + b, the m stands for _____________
Slope
In the equation, y = mx + b, the b stands for _____________
y-intercept
In the equation y = 3x + 7, the slope is _______________
3
In the equation y = 3x + 7, the y intercept is _______________
7
In the equation y = −2x − 6, the slope is ________________
−2
In the equation, y = −2x − 6, the y intercept is _____________
−6
Look at the graph for problem #12 on page 218. What is the equation in slope intercept form?
y = −1/5 x + 1
Look at the graph for problem #14 on page 218. What is the equation in slope intercept form?
y = −2 x + 3
Look at the graph for problem #34 on page 219. What is the equation in slope intercept form?
y = −4/7 x − 2
Given the point (1, 9) and the slope 4, write the equation in slope intercept form
y = 4x + 5
Given the point (1, 3) and (−3, −5), write the equation in slope intercept form
y = 2x + 1
Write the equation in slope intercept form: 2x + 4y = 12
y = −1/2x + 3
Look at the graph for problem #40 on page 235. Write the equation in point slope form
y − 3 = 4(x − 1)
Look at the graph for problem #42 on page 235. Write the equation in point slope form
y − 7 = −4/3(x + 3)
Given the point (2, 2) and m = −3, write the equation in point slope form
y − 2 = −3(x − 2)
Given the point (−8, 5) and m = −2/5, write the equation in point slope form
y − 5 = −2/5(x + 8)
The point slope form of a linear equation is ________
y - y1 = m(x − x1)
The slope intercept form of a linear equation is ____
y = mx + b
Write the equation in standard form: y − 11 = 3(x − 2)
3x − y = −5
Write the equation in standard form: y − 10 = −(x − 2)
x + y = 12
Write the equation in slope intercept form:. . . y + 2 = 4(x + 2)
y = 4x + 6
Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . y = −2x and 2x + y = 3
Parallel
Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 3x + 5y = 10 and 5x − 3y = −6
Perpendicular
Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 2x + 5y = 15 and 3x + 5y = 15
Neither
What form should you put lines in to determine if they are parallel, perpendicular, or neither?
Slope intercept form
What is true about the slopes of parallel lines?
The slopes of parallel lines are the same
What is true about the slopes of perpendicular lines?
The product of slopes of perpendicular lines is −1. (Slopes of perpendicular lines are opposite reciprocals)
Write the equations for two lines that are parallel.
There are many answers. An example would by y = 2x and y = 2x + 7.
Write the equations for two lines that are perpendicular.
There are many answers. An example would by y = 2x and y = −1/2 x + 6. The product of the two slopes has to be −1
What is true about any horizontal line and a vertical line?
They are perpendicular
Write an equation in slope intercept form for the line that passes through (−2, 2) and is perpendicular to y = −1/3 x + 9.
y = 3x + 8
Write an equation in slope intercept form for the line that passes through (3, 2) and is parallel r to y = x + 5.
y = x − 1
Write an equation in slope intercept form for the line that passes through (10, 5) and is perpendicular to 5x + 4y = 8.
y = 4/5x − 3
Write an equation in slope intercept form for the line that passes through (−1, −2) and is parallel to 3x − y = 5.
y = 3x + 1
Describe how you would graph y = 1/3 x + 2 using the slope and the y interept.
Put a dot on the y-axis on the number 2. Count a slope of 1/3 by going up 1 and right 3 or down 1 and left 3. Count the slope two or three times and then draw the line.
Graph 3x − y < 2
Solve the equation for y (slope intercept form) Graph the line with a dotted line. Check a point to see what side to shade. See a graph for this inequality on page 315
Graph x + 5y ≤ 10
Solve the equation for y (slope intercept form) Graph the line with a solid line. Check a point to see what side to shade. See a graph for this inequality on page 316
Solve x + 11 > 16 Graph the inequality.
{x|x > 5} The graph of the number line is an open circle on five and shading to the right.
Solve 3x + 17 < 4x Graph the inequality
{x|x > 17} The graph is a number line with an open circle on 17 and shading to the right.
Solve the compound inequality x − 5 < − 4 or x − 5 ≥ 1 Graph the compound inequality.
{x | x < 1 or x ≥ 6 The graph is an open circle on 1 and shading to the left and a closed circle on 6 and shading to the right.
Solve the inequality −2x + 4 > −6 Graph the inequality.
{x | x < 5} The graph is a number line with an open circle on 5 and shading to the left.
Solve the compound inequality 4 < x + 6 and x + 6 < 5 Graph the inequality
{x | −2 < x < −1 The graph is a number line with an open circle on negative two and an open circle on negative one and shading between
Write a compound inequality and solve: A number minus one is at most nine, or two times the number is at least twenty-four
x − 1 ≤ 9 or 2x ≥ 24 {x |x ≤ 10 or x ≥12}
Solve and graph the inequality x + 12 ≥ 8
{x |x ≥ − 4} The graph is a number line with a closed circle on negative four and shading to the right.
Solve and graph the inequality x − (−5) > −2
{x | x > − 7} The graph is a number line with an open circle on negative seven and shading to the right.
Wriite and solve in inequality: Twice a number minus 4 is less than three times the nunmber.
2x − 4 < 3x {x | x > − 4}
Solve x/6 ≤ 2
{x | x ≤ 12}
Solve −8x < −64
{x | x > 8}
Solve 6x + 12 < 8 + 8x
{x | x> 2}
Solve −8x − 3 < 18 − x
{x | x > − 3}
Solve 2(x + 3) ≥ 16
{x |x ≥ 5}
Solve −5 − x/6 ≥ −9
{x |x ≤ 24 }
Graph x > 3 or x ≤ 0
Open circle on three and shading to the right. Closed circle on zero and shading to the left.
Graph x ≤ 3 and ≥ −2
Closed circle on 3 and closed circle on negative two with shading between
Solve and graph |x|< 3
{x |−3 < x < 3} Open circle on three and negative three with shading between
Solve and graph |x − 4|< 4
{x | 0 < x < 8} The number line has an open circle on zero and an open circle on eight with shading between
Use an augmented matrix to solve the system of equations: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2x − y = 7 and −x + 3y = −11
(2, −3)
State the dimensions of the matrix and identify the circled element for problem #12 on page 372
2 X 5 The circled three is in the second row and first column
Subtract the two matrices for problem #18 on page 373. If the matrix does not exist write impossible
Impossible
Perform the indicated matrix operations for problem #28 on page 374. If the matrix does not exist, write impossible.
First row of matrix −9 4 second row of matrix −3 67 This is a 2 X 2 matrix
Use elimination to solve the system of equations: x + 4y = 11 and x − 6y = 11
(11, 0)
Use elimination to solve the system of equations: 2x − y = −1 and 3x − 2y = 1
(−3,−5)
Use an augmented matrix to solve the system of equations: x + 4y = 19 and −3x − 2y= −7
(−1 , 5)
Graph y > −2x + 1 and y ≤ x + 3
See how the graph should appear on page 382
Sketch a system of equations that has one solution.
See the concept summary on page 333.
Use substitution to solve the system of equations: y = 4x and x + y = 5
(1, 4)
Use substitution to solve the system of equations: 3x − y = 4 and 2x − 3y = −9
(3, 5)
Sketch a system of equations that has no solution.
See the concept summary on page 333.
Solve the system of equations by graphing . . . . x + 3y = −3 and x − 3y = −3
(−3, 0)
Solve the system of equations by graphing: . . . y = 2x + 3 and 3y = 6x − 6
No solution
Sketch a system of equations that has many solutions.
See the concept summary on page 333.
Solve the system of inequalities by graphing: 3x − y ≥ 2 and 3x − y < − 5
See the graph on page 383
Solve using elimination: . . . . −3x −4y = −1 and 3x− y =−4
(−1, 1)
Solve using elimination: . . . . . . . . . . . . . . . . −3x −4y = −4 and x + 3y = −1
(−4, −2)
Find the degree of the polynomial 10x³y⁵
8
Simplify. Assume no denominator is equal to zero. −15 w⁰u−¹/5u³
−3/u⁴
Simplify (−3ab⁴)³
−27a³b¹²
Simplify. Assume no denominator is equal to zero. (3x³y)²/27x²
x⁴y²/3
²Simplify. Assume no denominator is equal to zero. (4x/3x²)−²
9x²/16
Simplify: (2xy)²(−3x²)(4y⁴)
−48x⁴y⁶
Evaluate. Express in scientific and standard form (4.9 X 10−³)/(4.0 X 10−⁵)
Scientific 1.96 X 10−⁷and standar 0.000000196
Evaluate. Express in scientific and standard form (4.8 X 10⁴)(6 X 10⁶)
Scientific 2.88 X 10¹¹ and standard 288,000,000,000
Find the degree of the polynomial 5x²y + 7xy⁶− 3xy
7
Find the product (x + 9)²
x² + 18x + 81
Find the product (3x − 2)(3x + 2)
9x² − 12x + 4
Find the product (x − 7)(x + 5)
x² − 2x − 35
Find the difference. (3x² − 7x + 5) − (−x² + 4x)
4x² − 11x + 5
Solve 2(a − 3) = 3(−2a + 6)
a = 3
Express 1,900,000 in scientific notation
1.9 X 10⁶
Write 4 − x + 3x³ − 2x² in standard form and identify the leading coefficient
3x³ − 2x² −x + 4 The leading coefficient is 3
Find the volume of a cube whose length, width, and heighth have a measure of 3x⁵
27x¹⁵
Express the number 158 X 10⁻⁷in scientific notation
1.58 X 10⁻⁵
Express the number 0,00005816 in scientific notation
5.816 X 10⁻⁵
Find the product (3x − 1)²
9x²− 6x + 1
Find the sum (−4p² − p + 9) + (p²+ 3p −1)
−3p²+ 2p + 8
Find the product (5a − 2)(2a − 3)
10a² − 19a + 6
Express 0.000000058 in scientific notation
5.8 X 10⁻⁸
Find the difference. (3a − 5)) − (5a + 1)
−2a − 6
Simplify (x⁷)⁴
x²⁸
Simplify (−4xy)³(−2x²)³
512x⁹y³
Find (n −4)(n − 6)
n² − 10n + 24
Solve 2(4x + 3) + 2 = −4(x + 1)
x = −1
Find the degree of the polynomial 2x² + 3x + 7
2
Simplify x⁹/x²
x⁷
Find 5m²(2m³ −m)
10m⁵ − 5m³
Simplify x³ ∙ x²
x⁵
Simplify m⁴r²/mr⁴
m³/r²
Factor and solve 2x² + 7x + 3 = 0
Factors are (2x + 1)(x + 3) = 0 Solutions are −3 and −1/2
Solve the equation x² = 10x
Factors are x(x − 10) = 0 Solutions are 0 and 10
Factor and solve p² + 5p − 84 = 0
Factors are (p + 12)(p − 7) = 0 Solutions are −12 and 7
Find the GCF 40xy², 56x3y², 124x²y³
4xy²
Factor 8m − 6
2(4m − 3)
Factor 2t² + 9t − 5
(t+ 5)(2t −1)
Factor and solve h²− 17h = −60
Factors are (h − 12) (h − 5) = 0 Solutions are 5 and 12
Factor the polynomial 9x² −3xy + 6x − 2y
(3x + 2)(3x− y)
Factor completely 3a² + 30a + 63
3(a + 7)(a + 3)
Factor 16p² − 36
(4p − 6)(4p + 6)
Factor y² − 6y +8
(y − 2)(y − 4)
Fator 2x² + 5x + 2
(x + 2)(2x + 1)
Solve the equation 2x(x − 3) = 0
0 and 3
Factor n² + 7n + 12
(n + 4)(n + 3)
Factor the monomial completely −38a²b
−1 ∙ 2 ∙ 19 ∙ a ∙ a ∙ b
Find the GCF 88a³d, 40a²d², 32a²d
8a²d
Factor 4x²− 25
(2x − 5)(2x + 5)
Use the distributive property to factor 24x + 48y = 0
12(x + 2y)
Factor and solve x²− 16 = 0
Factors are (x − 4) (x + 4)) Solutions are 4 and −4
Factor the monomial completely 42g²h
2 ∙ 3 ∙ 7 ∙ g ∙ g ∙h
Factor and solve 25p² − 16 = 0
Factors are (5x − 4)(5x + 4) = 0 Solutions are 4/5 and −4/5
Factor and solve 5d² − 22d + 8 = 0
Factors are (d − 4)(5d − 2) = 0 Solutions are 4 and 2/5
Is the equation y = 300(1.09)ⁿ exponential growth or decay
Growth
Solve by completing the square. Round to the nearest tenth if necessary x²+ 6x = 7
−7 and 1
Write the equation of the function that would translate the graph of x² over the x-axis, stretch it vertically by a factor of 2 and translate it down 3
y = −2x² − 3
Describe how the graph of the function is related to the graph of f(x) = x² g(x) = x² + 9
Translates up 9
Solve x² − 2x − 8 by graphing. What are the domain and range?
The axis of symmetry is 1. The vertex is (1, −9). Some points in the table may be (1, −9), (0, −8), (2, −8), (4, 0), (−2, 0) The solutions are 4 and −2. See the graph on page 537.Domain reals and range y ≥ −9
Solve the equation by using the quadratic formula. Round to the nearest tenth if necessary x² + 8x + 7 = 0
−7 and −1
Determine whether the sequence is arithmetic, geometric, or neither 1, −5 −11, −17 . . .
Arithmetic
What is a geometric sequence?
A geometric sequence has a first term that is not zero and each term after the first is found by multiplying the previous term by a nonero constant
Is the equation y = 300(.95)t exponential growth or decay
Decay
What is an arithmetic sequence?
An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. The next term is found by adding the same positive or negative number to the preceding term.
Write an equation to find the nth term of the sequence −2, 10, −50... and then use the equation to find the eleventh term
a₁₁ = −2 ∙ (−5)ⁿ⁻¹ The eleventh term is −19,531,250
Solve x² + 6x + 8 = 0 by graphing and what are the domain and range.
The axis of symmetry is −3. The vertex is (−3,−1). Some points in the table may be (−3, −1), (−2, 0), (−4, 0), (−1, 3), (−5, 3) The solutions are − 4 and −2. Domain reals, Range y ≥ −1
The value of a new television depreciates by about 7% per year. You purchase a \$3,000 TV. What is its value after 4 years. Write and solve an expontential equation to solve.
y = 3000(.93)⁴ In four years, the value of the TV is about \$2244.16
\$20,000 is invested at an interest rate of 5.2%. The interest is compounded quarterly. Write and evaluate an equation to determine how much money will be in the account in 10 years.
y = (20000)(1.013)⁴⁰ The amount would be \$33528.01
Sketch a graph that has a minimum at the point (4, −2) and has roots (or solutions) at 2 and 6
Put a point on the minimum of (4, −2) Put points on the x-axis on 2 and 6 and connect the parabola
Describe how the graph of the function is related to the graph of f(x) = x² g(x) = −2x²
Reflected over the x-axis and stretched vertically
Is the equation y = x² + 2x + 7 linear, quadratic or exponential?
Is the equation y = 1/2x + 5 linear, quadratic, or exponential?
Linear
Is the equation y = 5ⁿ linear, quadratic, or exponential?
Exponential
Graph y = 3ⁿ
Some points are (0, 0), (1, 3), (2, 9), (−1, 1/3), (−2, 1/9) See the graph on page 567
Determine the next three terms in the geometric sequence 2, 6, 18 . . .
54, 162, 486
Solve by completing the square. Round to the nearest tenth if necessary x² − 8x + 15 = 0
3 and 5
Solve by using the quadratic formula. Round to the nearest tenth if necessary x² + 5x = 6
−6, 1
Sketch a quadratic equation that has one root (solution).
The parabola touches the x-axis at one point. See page 537
Sketch a quadratic equation that has two roots (solutions).
The parabola touches the x-axis at two points. See page 537
Sketch a quadratic equation that has no roots (solutions)
The parabola does not touch the x-axis. See page 537.