Solving Quadratics
Solving Equations in One Variable
Real World Problems + Translating Verbal Expressions
Transformations
Exponential Relationships
100
Solve the quadratic equation: 6x^2+7x-3=0
X= 1/3 or -1.5
100
4x+1 = 4x+2
Infinite solutions/all real numbers
100
Write an expression to represent the following:
One more than the difference of three times a number and nine
1 + (3x - 9)
100
f(x - 2)
100
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number population of the town after 9 years.
Approximately 42,640 people
200
X^2+15x-16=0
X=1 or -16
200
25 = 3 + 2(x-12) + 4
x = 21
200
The sum of three times a number and 2 less than 4 times that same number is 15. Write an equation that could be used to find the value of the number, n.
3n + (4n - 2) = 15
200
f(x) + 2
200
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years? Round to the nearest cent.
$1,751.21
300
Solve the equation: 15x^2-26x-21=0
X=7/3 or -3/5
300
2(3x-1) = 3x + 15 + x + 11
x = 14
300
The length of a rectangle is 40 in, and its area is to be less than 360 in2. What can be said about the width of the rectangle?
What is it must be less than 9 inches (w < 9)
300
The function f(x) = x2+3x+4 underwent a transformation to become g(x) = -2f(x+3) + 1.List all the transformations.
1. Reflect across the x-axis
2. Narrower (vertical stretch)
3. Shift left 3
4. Shift up 1
300
The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth model and find the population after 10 years.
f(x) = 20,000(1.13)x
f(10) = 20,000(1.13)10 and population of 67,891
400
Solve the equation: x(10x - 1) = 2
X=0.5, x = -0.4
400
5(3x + 7) – 3 = 2(4x + 23)
x = 2
400
The leading scorer in your basketball division finished the season with an average of 20 points per game for 25 games. As the division's second leading scorer, you have a 19.5 point per game average for 24 games. You have yet to play your last game. How many points must you score in the last game of the season to overtake the division's leading scorer?
What is 32 points or more (p > 32).
400
Consider the function f(x) = 1/3(x - 3)2 + 1. To reflect the graph over the x-axis, which of the following numbers would have to be opposite?
1/3 - that would cause a reflection
400
Given y = 250(1.2)^t, what is the percent increase per x?
1.20 = 120% kept
20% increase
500
2y^2+4y=7y+8
Y= 3+(square root)73/4 or 3-(square root)73/4
500
1/4(3x + 7) = 20
x = 73/3
x = 24 and 1/3
x = 24.333333.....
500
The base of a triangle is 10 inches. Its height is (x + 4) inches. Its area must be at least 60 in2. What are the possible values of x? (Area of a triangle = 1/2 base * height)
What is x ≥ 8
500
The function f(x) = x2 + 4x + 3 undergoes a transformation to become g(x) = f(x - 3).
Part A: What are the roots of g(x)?
Part B: What is the vertex of g(x)?
Shift right 3
Original roots: x = {-3, -1}. New roots: x = {0, 2}
Original vertex: (-2, -1). New vertex: (1, -1)
500
(2hj2k-2h4j-1k4)0/(2h-3j-4k-2)
(h3j4k2)/(2)