Factoring and Finding Zeros of Quadratics
The trinomial x2 -14x +49 can be expressed as:
1) (x-7)2
2) (x+7)2
3) (x-7) (x+7)
4) (x-7) (x+2)
1) (x-7)2
A function is defined as [ (0,1), (2,3), (5,8), (7,2)]. Isaac is asked to create one more ordered pair for the function. Which ordered pair can he add to the set to keep it a function?
1) (0,2) 3) (7,0)
2) (5,3) 4) (1,3)
4) (1,3)
What is the y-intercept of the line that passed through the points (-1, 5) and (2, -1)?
1) -1 3) 3
2) -2 4) 5
3) 3
What is the solution to the system of equations below?
y = 2x + 8
3 (-2x +y) = 12
1) no solution 3) (-1,6)
2) infinite solutions 4) (1/2, 9)
1) no solution
Which product is equivalent to 4x2 - 3x - 27?
1) (2x + 9) (2x - 3)
2) (2x - 9) (2x + 3)
3) (4x + 9) (x - 3)
4) (4x - 9) (x + 3)
3) (4x + 9) (x - 3)
If f(x) = x2 +2, which interval describes the range of this function?
1) ( - oo , oo) 3) [ 2, oo)
2) [ 0, oo) 4) (-oo, 2]
3) [ 2, oo)
Solve 5(x-2) </ 3x + 20 algebraically.
x </ -5
Which system has the same solution as the system below?
x + 3y = 10
-2x -2y = 4
1) -x + y =6 3) x + y =6
2x + 6y = 20 2x + 6y = 20
2) -x + y = 14 4) x + y =14
2x + 6y = 20 2x + 6y = 20
2) -x + y = 14
2x + 6y = 20
The expression 9m2 - 100 is equivalent to:
1) (3m - 10) (3m +10)
2) (3m - 10) (3m - 10)
3) (3m - 50) (3m +50)
4) (3m - 50) (3m - 50)
1) (3m - 10) (3m +10)
Given g(x) = x3 + 2x2 -x, evaluate g(-3).
g(-3) = -6
What linear equation represents a line that passes through the point (-3, -8)?
1) y = 2x - 2 3) y = 2x + 13
2) y = 2x - 8 4) y = 2x - 14
1) y = 2x - 2
Dana went shopping for plants to put in her garden. She bought three roses and two daisies for $31.88. Later that day, she went back and bought two roses and one daisy for $18.92.
If r represents the cost of one rose and d represents the cost of one daisy, write a system of equations that models this situation and use it to determine the cost of one rose and one daisy.
3r + 2d = 31.88
2r + d = 18.92
A rose costs $5.96 and a daisy costs $7.
Factor 2x2 + 16x - 18 completely.
2 (x+9) (x - 1)
or
2( x - 1) (x+9)
The domain of the function f(x) = x2 +x -12 is
1) ( -oo, 4]
2) (-oo, oo)
3) [-4, 3]
4) [3, oo)
2) (-oo, oo)
A tour bus can seat, at most, 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If a represents the number of adult tickets sold and c represents the number of child tickets sold, which system of inequalities models this situation if they make a profit?
1) a + c < 48 3) a + c < 48
18a + 12c > 650 18a + 12c <650
2) a + c </ 48 4) a + c </ 48
18a + 12c >/ 650 18a + 12c </650
2) a + c </ 48
18a + 12c >/ 650
Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 90 coins with a value of $17.55 inside of the bank.
If Dylan only collects dimes and quarters, write a system of equations in two variables or an equation in one variable that could be used to model this situation.
d + q = 90
0.10d + 0.25q = 17.55
The function r(x) is defined by the expression x2 +3x -18. Use factoring the determine the zeros of r(x).
x = -6 and x= 3
or
(-6,0) and (3,0)
If f(x) = (3x +4) / 2, then f(8) is
1) 21
2) 16
3) 14
4) 4
3) 14
Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. What inequality could be used to determine the number of dimes, d, she needs in her purse to be able to pay for lunch?
1) 1.75 + d >/ 3.00 3) 1.75 + d </ 3.00
2) 1.75 + 0.10d >/ 3.00 4) 1.75 + 0.10d </ 3.00
2) 1.75 + 0.10d >/ 3.00
Hannah went to the school store to buy supplies and spent $16. She bought four more pencils than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each.
If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought.
4 + x = # of pencils
x - 2 = # of erasers
x = pens
1.25x + 0.55 (x +4) + 0.75 (x-2) = 16