Domain & Range
Word Problems
Key Attributes
Factoring
Quadratic Formula
100
Determine the domain of this graph.
All Real Numbers
100
Caleb, Michael and Steven went to James Coney Island for lunch. Michael bought a drink, 2 hot dogs, and a basket of French fries and spent $10.50. Steven spent $9.75 on a hot dog, 2 baskets of French fries, and a drink. Caleb wasn’t very hungry, so he only bought a hot dog and a drink. Caleb spent $6.25. Let x = the cost of a hot dog, y = the cost of a basket of French fries, and z = the cost of a drink. Write a system of equations to represent this situation.
2x+y+z=10.50
x+2y+z=9.75
x+z=6.25
100
What are the zero(s) of this function?
-2 and 4
100
What terms have the same meaning as "solution to a quadratic equation."
x-intercepts, zeros, roots
100
2x^2-36x+160=0
x=10 and x=8
200
Determine the range of this function in inequality notation.
-8<y<=8
200
Billy’s Restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered 20 fewer roses than daisies. The total order came to $589.50.
c+r+d=200
1.50c+5.75r+2.60d=589.50
d=r-20
200
What is the equation of the axis of symmetry?
x=1
200
What are the roots of the equation x^2+9x+18=0
x=-3 and x=-6
200
x^2-16x=-55
x=11 and x=5
300
The trajectory of a potato launched from a potato cannon on the ground can be modeled by the parabola.
Using set builder notation, give the domain and range of the potato.
Domain: {x|0<=x<=4}
Range: {y|0<=y<=64}
300
Regal Cinema sells student, adult, and senior citizen movie tickets. Student tickets sell for $9.50, adult tickets are $12, and senior citizen tickets are $7.50. They sold a total of 2364 tickets last weekend and made a total of $18,260. The number of senior tickets sold was 12 less than twice the number of adult tickets sold. Write a system of equations to represent this situation. Be sure to define your variables.
s+a+c=2364
9.50s+12a+7.50c=18260
2a-12=c
300
The graph of the quadratic function y=0.25x^2+1.5x-6.75 is shown below.
Given the graph of the quadratic function, find the minimum on the interval [-1,5] .
-8
300
Given the equation, x^2+2x-24=0 . What are the roots of the equation?
-6 and 4
300
0=16x^2+20x-1
(-5+-sqrt29)/8
400
What is an appropriate range for x^2+2x-4=0
y>=-5
400
Julie’s little brother, Jacob, needed money. He asked Julie if he could have the money she had saved in her piggy bank. Julie told him that if he could figure out how many of each type of coin, she had that he could have the money. She gave him these clues: I have 20 less than dimes than quarters. The total amount of money is $20.55. There are 64 coins, and I only have dimes, nickels and quarters. Write a system of equations to help Jacob determine how many nickels, dimes, and quarters Julie has.
d+n+q=64
0.10d+0.05n+0.25q=20.55
d=q-20
400
Hannah correctly graphed a quadratic function and found that its vertex was (-3,-1) . Which of the following function(s) could she have graphed?
I. y=x^2+6x+8
II. y=x^2-6x+11
III. y=(x+3)^2-1
IV. y=(x-3)^2+1
I and III only
400
Solve the equation 3x^2-75=0
x=+-5
400
8x^2-12x+13=0
(3+-isqrt17)/4
500
What is the domain and range of the function f(x)=(x-6)^2-7 in interval notation?
Domain: (-oo,oo)
Range: [-7,oo)
500
Write your own problem and 3 equations to match. Include 3 variables and clearly define each variable.
Answers may vary.
500
Vertex:
Minimum:
Axis of Symmetry:
Vertex: (-6,-4)
Minimum: -4
Axis of symmetry: x=-6
500
Find the solutions to the quadratic below.
2x^2+12x=7x+7
x=-7/2 and x=1
500
Find the roots of the equation.
5x^2+6x+3=0
(5+-sqrt97)/6