7. Find the value of the discriminant and give the number of real solutions.
4(x2 + 5x) = 25
A) 0, one
B) 800, two
C) –800, none
D) 500, two
8. Find the value of the discriminant and give the number of real solutions.
3x2 + 6x – 6 = 0
A) 0, one
B) –36, none
C) 78, two
D) 108, two
11. True or False: The graph of every equation of the form y = ax2 + b, where a and b are real numbers and a is not zero, is a parabola with the y-axis as the axis of symmetry.
12. Find the equation of the axis of symmetry for the parabola given by y = –x2 + 6x – 13.
A) y = 4
B) x = –3
C) x = 3
D) x = 0
13. True or False: The graph of every equation of the form y = ax2 + b, where a and b are real numbers and a is not zero, is a parabola with a vertex (0, b).
14. Give the coordinates of the vertex for the parabola given by y = 6x2 + 24x + 29.
A) (2, 0)
B) (–2, 5)
C) (6, 0)
D) (6, 5)
15. Give the coordinates of the vertex for the parabola given by y = x2 – 6x + 7.
A) (3, –2)
B) (–3, 34)
C) (3, 19)
D) (6, –3)
18. Use the graph of the related parabola to estimate the solutions to 0 = x2 + 5x +1. Round answers to three places.
A) {–0.209, 4.791}
B) {0, 1}
C) {–4.791, –0.209}
D) {0.209, 4.791}
19. Use the graph of the related parabola to estimate the solutions to 0 = x2 + 6x +1. Round answers to three places.
A) {0.172, 5.828}
B) {–5.828, –0.172}
C) {–3, 3)
D) {–2.828, 2.828}
20. The revenue R in dollars for the sale of x items at Joe's Dollar Store can be modeled by the equation R = 1400x – 5x2. What number of items would provide a revenue of $16,080?
A) 140 items
B) 12 items, 1388 items
C) 11 items, 292 items
D) 12 items, 268 items
21. A small company's weekly profit P, in dollars, is related to the number of items sold x by P(x) = –0.4x2 + 60x + 1250. Find the number of items that should be sold each week in order to maximize the profit. Then find the amount of that weekly profit.
A) 30 items, $2,690
B) 60 items, $3,410
C) 75 items, $3,500
D) 150 items, $32,750