Download Review 2/1-2

Review 2/1-2
Using the graph of f(x) = x2 as a guide, describe the transformations.
1. f(x) = 2(x + 3)2 – 4
2. h(x) = 3(x – 5)2 + 7
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3. g(x) = ½(x + 4) + 5
4. J(x) = ¼ (x – 6) – 8
Use the description to write each quadratic function in vertex form.
5. f(x) = x2 is vertically stretched by a factor of 2, translated up 3 and right 4.
6. f(x) = x2 is horizontally compressed by a factor of 1/3, translated down 4 and left 5.
7. f(x) = x2 is vertically compressed by a factor of ¼, translated down 5 and left 6.
8. f(x) = x2 is horizontally stretched by a factor of 5, translated up 7 and right 3.
For each function, (a) determine whether the graph opens up or down.
(b) determine whether the graph has a maximum or minimum.
(c) find the axis of symmetry, then graph it.
(d) find the vertex, then plot it.
(e) determine the domain and range of the function.
(f) find the y-intercept, plot it. Plot its symmetric counterpart.
(g) graph the function.
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9. f(x) = x – 5x + 6
10. f(x) = 7x – x2
11. f(x) = -(x – 4)2 + 3
12. f(x) = (x – 3)2
13. A record label uses the following function to model the sales of a new release, a(t) = -90t2 + 8100t.
The number of albums sold is a function of time, t, in days. On which day were the most albums
sold? What is the maximum number of albums sold on that day?
14. An airline sells a 3-day vacation package. Sales from this vacation package can be modeled by the
quadratic function s(p) = -40p2 + 32000p. Sales are dependent on the price, p, of the package. If
the price is set too high, the package won’t sell, but if the price is too low, prospective buyers will
think it is a scam. At what price, p, does the company have the greatest sales. What is the
maximum sales at this price?
Answers:
1. Vertical stretch by a factor of 2, translated left 3 and down 4.
2. Vertical stretch by a factor of 3, translated right 5 and up 7.
3. Vertical compression by a factor of ½, translated left 4 and up 5.
4. Vertical compression by a factor of 1/4, translated right 6 and down 8.
5. g(x) = 2(x – 4)2 + 3
6. g(x) = [3(x + 5)]2 – 4
7. g(x) = ¼ (x + 6)2 – 5
8. g(x) = [1/5 (x – 3)]2 + 7
9. (a) up
(b) minimum
(c) x = 2.5
(d) (2.5, -0.25)
(e) domain: all real numbers range: {y|y ≥ -0.25}
(f) (0, 6)
10. (a) down
(b) maximum
(c) x = 3.5
(d) (3.5, 12.25)
(e) domain: all real numbers range: {y|y ≤ 12.25}
(f)(0, 0)
11. (a) down
(b) maximum
(c) x = 4
(d) (4, 3)
(e) domain: all real numbers range: {y|y ≤ 12.25}
(f) (0, -13)
12. (a) up
(b) minimum
(c) x = 3
(d) (3, 0)
(e) domain: all real numbers range: {y|y ≥ 0}
(f) (0, 9)
13. t = 45th day
a(t) = 182,250 albums
14. p = $400
s(p) = $6,400,000