1. Quadratic Functions and Their Properties
Section 4.3
Quadratic Functions and Their Properties

3. R(p) = (21,000 – 150p)p
= -150p2 +21,000p

5. OBJECTIVE 1

9. vertex: (-2, -3) axis of symmetry: x = -2

11. OBJECTIVE 2

13. Without graphing, locate the vertex and axis of symmetry of the parabola defined by Does it open up or down?
Vertex: (1,4)
Axis of symmetry: x = 1
Opens Down

14. OBJECTIVE 3

17. Vertex: (-2,-17)
x-intercepts: (-4.38, 0), (0.38, 0)
y-intercept: (0, -5)
Domain: All Reals, Range y
Decreasing: (-∞,-2), Increasing: (-2,∞)

18. Vertex: (-2,0) x-intercepts: (-2, 0) y-intercept: (0, 4)
Domain: All Reals, Range y ≥ 0
Decreasing: (-∞,-2), Increasing: (-2,∞)

19. vertex: (2, 11)
x-intercepts: (-1.32, 0), (5.32 , 0)
y-intercept: (0, 7)

20. Domain: All Reals, Range y ≤ 11
Increasing: (-∞, 2), Decreasing: (2,∞)

23. Determine the quadratic function whose vertex is (-2, -5) and whose y intercept is – 1.
y = a(x - h)2 + k where (h, k) is the vertex
y = a[x – (-2)]2 + (-5) = a(x + 2)2 – 5
(0, -1): -1 = a(0 + 2)2 -5
-1 = 4a – 5
4 = 4a  a = 1
y = 1(x + 2)2 – 5 = x2 + 4x + 4 – 5 = x2 + 4x - 1

24. OBJECTIVE 4

25. Since a = -1 it will have a maximum at x =
So the maximum value is