Problem 1 :
In the xy plane, what is the distance between the two x-intercepts of the parabola
y = x^{2} - 3x - 10
(a) 3 (b) 5 (c) 7 (d) 10
Problem 2 :
What are the solutions to x^{2} + 4x + 2 = 0 ?
(a) -2 ± √2 (b) 2 ± √2 (c) -2 ± 2√2 (d) -4 ± 2√2
Problem 3 :
If a < 1 and 2a^{2} - 7a + 3 = 0, what is the value of a ?
Problem 4 :
3x^{2} + 10x = 8
If a and b are two solutions to the equation above and a > b, what is the value of b^{2} ?
Problem 5 :
What is the sum of solutions of (2x - 3)^{2} = 4x + 5 ?
Problem 6 :
y = -3 and y = x^{2} + cx
In the system of equations above, c is a constant. For which of the following values of c does the system of equations have exactly two real solutions ?
(a) -4 (b) 1 (c) 2 (d) 3
Problem 7 :
At which of the following points does the line with equation
y = 4
intersect the parabola
y = (x + 2)^{2} - 5
in the xy - plane ?
(a) (-1, 4) and (-5, 4) (b) (1, 4) and (-5, 4)
(c) (1, 4) and (5, 4) (d) (-11, 4) and (7, 4)
Problem 8 :
Which of the following equations represents the parabola shown in the xy-plane above ?
(a) y = (x - 3)^{2} - 8 (b) y = (x + 3)^{2} + 8
(c) y = 2(x - 3)^{2} - 8 (d) y = 2(x + 3)^{2} - 8
Problem 9 :
For what value of t does the equation v = 5t - t^{2}, result in the maximum value of v ?
Problem 10 :
P = m^{2} - 100 m - 120000
The monthly profit of a mattress company can be modeled by the equation above, where P is the profit in dollars, and m is the number of mattresses sold. What is the minimum number of mattresses the company must sell in a given month so that it does not lose money during that month ?
Problem 11 :
y = -3
y = ax^{2} + 4x - 4
In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution ?
(a) -4 (b) 1 (c) 2 (d) 4
Problem 12 :
f(x) = -x^{2} + 6x + 20
The function f is defined above. Which of the following equivalent forms of f(x) displays the maximum value of f as a constant or coefficient ?
(a) y = -(x - 3)^{2} + 11 (b) y = -(x + 3)^{2} + 29
(c) y = -(x + 3)^{2} + 11 (d) y = -(x + 3)^{2} + 29
Problem 13 :
y = a(x - .3)(x - k)
In the quadratic equation above, a and k are constants. If the graph of the equation in the xy plane is a parabola with vertex (5, -32), what is the value of a ?
Problem 14 :
In the xy plane, the line y = 2x + b intersects the parabola
y = x^{2} + bx + 5
at the point (3, k). If b is a constant, what is the value of k ?
1) d = 3
2) x =-2±√2
3) 1/2
4) b^{2} = 16
5) α+β = 4
6) c = -4
7) (1, 4) and (-5, 4).
8) y = 2(x - 3)^{2} - 8
9) 2.5
10) 400
11) a = -4
12) f(x) = -(x - 3)^{2} + 29
13) a = 8
14) k = 2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM