1. How do you find the maximum value of a quadratic function? For example: y=-x 2 +16x-19

2. In this lesson you will learn to rewrite a quadratic function to reveal the maximum value by completing the square.

3. Let’s Review Suppose we have y=-x 2 +16x-19

4. A Common Mistake y=- x 2 +16x-19 y=-1(x 2 -16x )-19 + - 64 (-64) y= -1 (x-8) 2 +45 -83 Add a number inside the bracket and distribute before you subtract to preserve equality!

5. Let’s Review Core Lesson y=-1(x 2 +2x )+15 (x+1) 2 +16 y=-x 2 -2x+15 A square number is always positive unless it’s zero.

6. Let’s Review Core Lesson y=-(x+1) 2 +16 =-(-1+1) 2 +16 =0 +16

7. Let’s Review Core Lesson ADDING a negative number to any number makes that number smaller so the function will have a maximum value when the square term is zero.

8. Let’s Review Core Lesson x-(x+1) 2 +16y -2 16 15 7 12 1 -(-1+1) 2 +16 -(-2+1) 2 +16 -(2+1) 2 +16 -(1+1) 2 +16 2 Maximum value of y=-x 2 -2x+15 is 16 when x= -1 y= -(x+1) 2 +16

9. In this lesson you have learned to rewrite a quadratic function to reveal the maximum value by completing the square.

10. Let’s Review Guided Practice Rewrite y=-x 2 +5x-7 by completing the square. What is the maximum value of this quadratic function?

11. Let’s Review Extension Activities Partner matching cards. Write each function and ordered pair on index cards. Shuffle all 12 cards then match each function with its equivalent form and corresponding maximum value. y=-x 2 +2x+3 y=-(x-1) 2 +4 (1,4) y=-x 2 +20x-80 y=-(x-10) 2 +20 (-10,20) y=-x 2 -14x-45 y=-(x+7) 2 +4 (-7,4) y=-x 2 +10x-4 y=-(x-5) 2 -4 (-9,+21)

12. Let’s Review Extension Activities Geometry. The table shows some possible dimensions of rectangles with a perimeter of 100 units. Complete the table. WidthLengthArea 1 49 248 3 4 1.Plot the points (width, area) on a graph. 2.Use your graphing calculator to find a model for the data set: A=

13. Let’s Review Extension Activities On a single-lane highway, the traffic flow F (in cars per hour) can be modeled by F=-0.313C2+50C where C is the traffic concentration (in cars per mile). For what traffic concentration is traffic flow maximized? What is the maximum traffic flow? z L

14. Let’s Review Quick Quiz Rewrite each function to find its maximum value by completing the square.  y=-x 2 -8x+9  y=-x 2 +5x+6