1. 3.1

2. Standard (vertex) form General form

3.  Standard (vertex) form f(x)=a(x-h) 2 +k ◦ Open up or down? Max or min? ◦ Vertex is (h, k) ◦ Find x-intercepts ◦ Find y-intercept by figuring f(0) ◦ Plot the points, add more points if necessary (remember symmetry) ◦ The domain is (-∞,∞)

4.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range

5.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range

6.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range Standard form:

7.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range Standard form:

8.  General form f(x)=ax 2 +bx + c ◦ Open up or down? Max or min? ◦ x- value of vertex is –b/2a. Plug in for y-value. ◦ Find x-intercepts ◦ Find y-intercept by figuring f(0) ◦ Plot the points, add more points if necessary (remember symmetry) ◦ The domain is (-∞,∞)

9.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range General form:

10.  U/D?  Vertex  X-int.  Y-int  Graph it  Domain  Range General form:

11. Maximizing and minimizing

12.  The function f(x) = 0.4x 2 – 36x + 1000 models the number of accidents, f(x), per 50 million miles driven, for drivers x years old, where 16 ≤ x ≤ 74. What is the age of a driver having the least number of car accidents? What is the minimum number of car accidents per 50 million miles driven?

13.  Maximizing or minimizing quadratic functions ◦ What is the quantity to be maximized/minimized? ◦ Express the quantity as a function in one variable. ◦ Write the function in general form. ◦ Find the vertex of the function. ◦ Use the vertex to help answer the question.

14.  Among all pairs of numbers whose difference is 10, find a pair whose product is as small as possible. What is the minimum product? ◦ Minimize what? ◦ Write with one variable: ◦ Put in general form: ◦ Find vertex: ◦ Answer question:

15.  Among all pairs of numbers whose difference is 8, find a pair whose product is as small as possible. What is the minimum product? ◦ Minimize what? ◦ Write with one variable: ◦ Put in general form: ◦ Find vertex: ◦ Answer question: Applications of quadratic functions

16.  You have 100 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? ◦ Maximize what? ◦ Write with one variable: ◦ Put in general form: ◦ Find vertex: ◦ Answer question: Applications of quadratic functions

17.  You have 120 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? ◦ Maximize what? ◦ Write with one variable: ◦ Put in general form: ◦ Find vertex: ◦ Answer question: Applications of quadratic functions