Chapter 4 Review
1a) −5𝑥 + 4 = 0
-4 -4
- 5x =- 4
Answer: x =
−𝟒
−𝟓
or
𝟒
𝟓
1b) −5𝑥 + 4 > 0
-4 -4
- 5x > -4 (divide both sides by – 5 and switch
direction of sign because divide by
Negative
Answer: 𝒙 <
𝟒
𝟓
1c) 3x – 12 = - 5x + 4
+5x + 12 + 5x + 12
8x = 16
Answer: x = 2
1d) -5x + 4 < 3x – 12
-3x -4 -3x - 4
-8x < -16 (divide by -2 and switch direction
of sign since divide by negative
Answer: x > 2
2a) create two points. My points will be of the form (Time, Value)
(8,2000) and (0,50000) are my points.
The second point says when the tv’s are 0 years old they are worth $50,000. now find m 𝑚 = 𝑚 =
50000−2000
0−8
48000
−8
= −6000 so m = -6000
Now find b: use the equation y = mx+ b and ( m = -6000 x = 0 y = 50000)
50000 = -6000*0 + b
50000 = b
Acceptable answer: y = -6000x + 50,000 answer may be written using function notation. I can also change the letter x to the letter t to stand for time. better answer: V(t) = -6000t + 50,000
2b) replace the t with 6 and find the value
V(6) = -6000*6 + 50000
V(6) = 14000
Answer: $14,000

3a) Create two points of the form (Price, units rented)
(1000 , 1000) (1300, 900)
Now find m: 𝑚 =
900−1000
1300−1000
=
−100
300
=
−1
3
Next find b: use equation y = mx+b and m =
−1
3
, x = 1000 , y =1000
1000 =
−1
3
∗ 1000 + 𝑏
3 ∗ 1000 = 3 ∗
−1
3
∗ 1000 + 3 ∗ 𝑏
3000 = −1000 + 3𝑏
+1000 +1000
4000 = 3b 𝑏 =
4000
3
Answer: 𝒚 =
−𝟏 𝒑 +
𝟑
𝟒𝟎𝟎𝟎
𝟑
(I used p for price instead of x)
3b) plug $1200 for p and solve for y 𝑦 =
−1
3
∗ 1200 +
4000
3
I got 933.333333 when I used my calculator. I need to round this answer.
Answer: 933 units will be rented
3c) Let y = 800 and solve for p.
800 =
−1 𝑝 +
3
4000
3
−3 ∗ 800 = −3 ∗
−1
3 𝑝 + −3 ∗
4000
3
-2400 = 1p – 4000
1600 = p
Answer: a price of $1600 will cause 800 units to be rented

4a) use your calculator to plot the points (0, 13.70) (1, 13.12) (2, 12.71) …… (9, 9.53), you don’t need to show the graph.
4b) I used the linreg(ax+b) feature on my calculator to get this equation.
Answer: y = -.46x + 13.68
4c) This equation is a good fit since the value of |𝒓| >. 𝟖𝟎
4d) here is a graph, although it is not asked for.
4e) plug in 13 for x: I got 13 by doing this subtraction: 2000 – 1987 y = -.46*13 + 13.68 y = 7.7
Answer: there were 7.7 thousand insured commercial banks in 2000.
5a) h(x) = 2(x+1) 2 + 3 the +1 inside the parenthesis shifts 1 unit to the left, the + 3 after the parenthesis moves up 3 units the 2 in front of the parenthesis stretches the graph vertically (this is not needed in your answer
Answer: left 1, up 3, vertically stretched

5b) x
1
0
-1
-2
-3 h(x)
11
5
3
5
11
5c) domain for all parabolas (−∞, ∞) , to compute the range the graph needs to be extended to the top of the y-axis. Range will be of the form [y-coordinate of bottom point, ∞)
Answer: Domain (−∞, ∞) Range [𝟑, ∞)
5d) The graph is increasing to the right of the vertex, and decreasing to the left of the vertex:
Answer: increasing (−𝟏, ∞) decreasing (−∞, −𝟏)
5d) there is no maximum point
5e) The vertex is the minimum point
Answer: a local minimum occurs at x = -1, the minimum value is y = 3
6a) The + 2 in the parenthesis shifts left 2 the – 4 moves down 4 the ½ compresses vertically (you are not responsible for this part of the answer)
Answer: left 2, down 4, vertically compressed

6b) x
0
-1
-2
-3
-4 g(x)
-2
-3.5
-4
-3.5
-2
6c) domain for all parabolas (−∞, ∞) , to compute the range the graph needs to be extended to the top of the y-axis. Range will be of the form [y-coordinate of bottom point, ∞)
Answer: Domain (−∞, ∞) Range [−𝟒, ∞)
6d) The graph is increasing to the right of the vertex, and decreasing to the left of the vertex:
Answer: increasing (−𝟐, ∞) decreasing (−∞, −𝟐)
6d) there is no maximum point
6f) The vertex is the minimum point
Answer: a local minimum occurs at x = -2, the minimum value is y = -4
7a) The (-) in front of the 3 reflects over x-axis the + 8 moves up 8 the 3 stretches vertically ( you are not responsible for this on the test)
Answer: reflected over x-axis, up 8 , vertically stretched

7b) x
2
1
0
-1
-2
8
5
-4 m(x)
-4
5
7c) domain for all parabolas (−∞, ∞) , to compute the range the graph needs to be extended to the bottom of the y-axis. Range will be of the form (−∞, 𝑦 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝑡𝑜𝑝 𝑝𝑜𝑖𝑛𝑡]
Answer: Domain (−∞, ∞) Range (−∞, 𝟖]
7d) The graph is increasing to the left of the vertex, and decreasing to the rigth of the vertex:
Answer: decreasing (𝟎, ∞) increasing (−∞, 𝟎)
7e) The vertex is a maximum point
Answer: a local maximum occurs at x = 0, the maximum value is y = 8
7f) there is no minimum point

8a) group x’s: m(x) = (x 2 - 4x ) + 5
Find C = (
1
2
∗ −4)
2
= (−2)
2
= 4
Add and subtract C m(x) = (x 2 – 4x + 4) + 5
– 4 factor / combine
Answer: m(x) = (x-2) 2 + 1
9a)
Group x’s h(x) = (-4x 2 + 16x ) - 6
Factor out -4 h(x) = -4(x 2 – 4x ) -6
Find C = (
1
2
∗ −4)
2
= 4
Add 4 inside parenthesis , this is really like subtracting 16 if you clear the parenthesis the +4 will become – 16, so I will add 16 outside the parenthesis h(x) = -4(x 2 – 4x +4) - 6 + 16 factor and combine
Answer: h(x) = -4(x-2) 2 + 10
9b)

10a) let h = and solve for t
0 = -16t 2 + 80t + 6 (divide by (-2) to make numbers smaller)
0 = 8t 2 – 40t – 3 (use quadratic formula with a = 8, b = -40, c = -3 𝑡 =
−(−40)±√(−40) 2 −4(8)(−3)
=
2∗8
40±√1696
16
=
40±41.18
16 𝑡 =
40+41.18
16
𝑜𝑟
40−40.18
16 t = 5.07 or -.01(this can’t be the answer as time must be positive)
Answer: 5.07 seconds
10b) ball reaches maximum height at x-coordinate of vertex a = -16 b = 80 x-coordinate of vertex =
−𝑏
2𝑎
=
−80
2∗−16
=
−80
−32
= 2.5
Answer: ball reaches maximum height at 2.5 seconds
10c) maximum height occurs at y-coordinate of vertex h = -16(2.5) 2 +80(2.5)+6 h = 106
Answer: Maximum height 106 feet
11a) replace h with 85 and solve for t
85 = -16t 2 + 96t + 5
-85 -85
0 = -16t 2 + 96t - 80 (divide by -16)
0 = t 2 – 6t + 5
0 = (t – 1) (t – 5)
Answer: height is 85 feet at 1 and 5 seconds

11b) replace h with 0 and solve for t using quadratic formula: a = -16 b = 96 c = 5 𝑡 =
−96±√96 2 −4(−16)(5)
2∗−16
=
−96±√9536
=
−32
−96±97.65
−32 𝑡 =
−96+97.65
−32 𝑜𝑟
−96−97.65
−32 t = -.05 (ignore as time must be positive) or t = 6.05 answer: it will take 6.05 seconds for object to return to the ground
11c) maximum height occurs at y-coordinate of vertex x-coordinate of vertex =
−𝑏
2𝑎
=
−96
2∗−16
= 3 y-coordinate of vertex = -16(3) 2 + 96(3) + 5 = 149 answer: 149 feet is maximum height
12a) plot points (1,5) (2,20) (3, 40) (4,25) and (5,5) do not need to show this graph
12b) use linreg and quadreg on calculator to get these answers.
Answer: linear equation y = .5x + 17.5 quadratic equation y = -7.5x
2 + 45.5x – 35
12c) the quadratic equation is clearly the better fit
12d) this graph does not need to be drawn

12e) max height occurs at y-coordinate of vertex x-coordinate of vertex =
−𝑏
2𝑎
=
−45.5
2∗−7.5
= 3.03
y-coordinate of vertex = -7.5(3.03) 2 + 45.5(3.03) – 35 = 34.008 answer: maximum height is about 34 feet (according to the equation)