1. Building Quadratic Models from Verbal Descriptions and Data
Section 4.4
Building Quadratic Models from Verbal Descriptions and Data

2. OBJECTIVE 1

3. The marketing department at Texas Instruments has found that, when
certain calculators are sold at a price of p dollars per unit, the number x of calculators sold is given by the demand equation
(a) R(p) = xp = (26,000 – 160p)p = -160p2 + 26,000p
Since x ≥ 0 we have 26, p ≥ 0  p ≤ So 0 ≤ p ≤
(c) Find vertex:
(d) R(81.25) = $1,056,250

4. x = 26, (81.25) = 13,000
(f)

5. 800 2x + 2w = 800 A = xw 2x + 2w = 800 2w = 800 – 2x w = 400 - x
A = xw = x(400 – x) = -x x
x = -b/2a = -400/2(-1) = 200
w = 400 – x = 400 – 200 = 200

6. Find the maximum height of the projectile.
= x2 + x + 500
(a)
Find the maximum height of the projectile.
How far from the base of the cliff will the projectile strike the water?
h(2500) = (2500)
= 1750 ft

7. (b) When it hits the water the height h = 0.
h(x) = x2 + x = 0
a = , b = 1, c = 500

9. Note: Use 0 and 6000 for min and max for x and use -300 and
2000 for min and max for y. Use scale of 1000 for both.

11. y = .0001193a2 Using vertex (0, 0) we get y = ax2
Using point (2100, 526) we get
y = a2

12. OBJECTIVE 2

15. bushels