1. Warm-up:
How do you decide if you would rather receive a payday using linear, quadratic, or exponential values?
Are there any circumstances you need to consider?
Varies...
Varies...

2. HW Check:

3. HW Check:

4. HW Check:

5. HW Check:

6. Next Year’s Gig AND Dorton Arena
M & 7.13
Next Year’s Gig AND Dorton Arena
Objectives:
Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction or two linear functions with multiplication.
Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior.

7. A x represents the number of people who will buy a ticket after x number of $1 price increases.

8. 30 + x represents the ticket price after x number of $1 price increases
J(x) = - 20x2+ 7,400x + 240,000
J(0) = 240,000; constant term
(-30, 0) and (400, 0). The x-intercepts represent the number of $1 increases in ticket prices that would result in $0 in income.

9. 8000 - 18x: number of people who will buy a ticket after x number of $1 price increases.
40 + x represents the ticket price after x number of $1 price increases
A(x) = - 18x2 + 7,280x + 320,000
$320,000
A(0) = 320,000, constant term

10. Y-intercept
The vertex is at (202.2, 1,056,088.9). This means that the ticket price should be increased by $ $40 + $202.20= $242.20
The y-value of the vertex is the maximum income - $1,056,089.

11. -38x x
$320,000
$240,000
$560,000
$355,950
$276,500
$632,450
***Optional…Could skip and move on
$445,208
$366,720
$811,928
$198,912
$116,480
$315,392
$85,400 $0
$85,400

12. The y-intercept of B(x) is the sum of the y-intercepts of J(x) and A(x). Since we are adding the functions together, we add the y-values corresponding to the same x-values.
The maximum of B(x) is larger than the maximums of J(x) and A(x) but that is due to the context of adding incomes together. The maximum of the combined function is not generally the sum of the maximums of the original functions. This is because when you add two functions together, you are adding y-values for corresponding x-values. The vertices do not have the same x-values.

13. The parabola that opens up since the leading coefficient is positive.
D: (-∞, ∞) R: [ , ∞)
Intercepts (0,0) (127, 0)
Minimum at x = 63.5
Decreasing on (-∞, 63.5)
Increasing on (63.5, ∞)

14. Yes; -x x

15. Length : 8064.5 feet, width : 127 feet
Typo: #4 Should be f(x) = -x x
D: (-∞, ∞) R: (-∞, ]
Intercepts (0,0) (127, 0)
Minimum at x = 63.5
Increasing on (-∞, 63.5)
Decreasing on (63.5, ∞)
Length : feet, width : 127 feet

16. 67 and -67
No. The coefficients in the equation affect how fast the parabola increases/decreases.
Standard - The sign of leading coefficient tells you if the parabola opens up or down. The y-intercept is the constant term.
Factored - X-intercepts/zeros can be found by setting factors = 0

17. Exit ticket…
NONE

18. Classwork:
p , 27-28
HOMEWORK:
p RSG and p RSG