1. 3.2-2 – Maximum and Minimization

2. Recall… The standard form of a quadratic is… – y = The vertex form of a quadratic is… – g(x) =

3. As discussed previously, any given quadratic/parabola will have a vertex = highest or lowest point – Maximum when? – Minimum when?

4. In many applications, we are curious about the maximum or minimum – Examples; maximize profit, minimize costs, maximize items used, minimize waste Regardless, we need a way to evaluate for the maximum or minimum of any given quadratic

5. Vertex Formula Previously, we could use the vertex form But, as we found out, vertex form not always the easiest For a given quadratic written in the form y = ax 2 + bx + c, we can find the vertex with: – X coordinate = – Y coordinate =

6. Always make sure your quadratic is written in standard form, before hand Make note of the shape of your quadratic; does it fit the application well?

7. Example. A farmer wants to use 100 feet of spare fencing material to form a rectangular garden against the side of a long barn, with the barn being used as one side of the plot. How should he split up the fencing among the 3 sides to maximize the area of the garden?

8. Example. A ball is thrown upward with a velocity of 48 feet per second from the top of a 144 foot building. What is the maximum height of the ball? – H(t) = -16t 2 + 80t + 64

9. Example. The total cost of manufacturing a set of golf clubs is given as the function C(x) = 800 – 10x + 0.20x 2. How many golf clubs should be manufactured to minimize the costs.

10. Assignment Pg. 217 31-47 ODD