1. Sec 2.5 Quadratic Functions Maxima and Minima Objectives: Express a quadratic in vertex form. Find coordinates of vertex by completing the square. Find maximum and minimum values of a quadratic.

2. Standard Form A quadratic function f(x) = ax 2 + bx + c can be expressed in vertex form: f(x) = a(x – h) 2 + k by completing the square. The graph of f is a parabola with vertex (h, k).

3. Ex 1. Let f(x) = x 2 – 12x + 23. a)Express f in vertex form. b)Find the vertex.

4. Ex 2. Let f(x) = 3x 2 – 6x + 10 a)Express f in vertex form. b)Find the vertex.

5. Class Work 1.Let f(x) = 2x 2 +8x -5. a) Express f in vertex form b) Find the vertex.

6. Maximums and Minimums If a quadratic function has vertex (h, k), then the function has: A ______________value at the vertex if it opens ________. (if a > 0) A ______________ value at the vertex if it opens __________. (if a < 0) minimum up maximum down

7. Let f be a quadratic function with vertex form f(x) = a(x – h) 2 + k The maximum or minimum value of f occurs at ________ and is __________. x = hf(x) = k

8. Ex 3. Consider the quadratic function f(x) = 5x 2 – 30x + 49 a)Express f in vertex form. b) Find the minimum value of f.

9. Class Work 2. Consider the quadratic function f(x) = 2x 2 – 20x + 53 a)Express f in vertex form. b) Find the minimum value of f.

10. Class Work 3. Consider the quadratic function f(x) = –2x 2 + 4x + 5 a)Express f in vertex form. b) Find the maximum value of f.

11. Finding max and min without completing the square. The maximum or minimum value of a quadratic function f(x) = ax 2 + bx + c occurs at: ________

12. Ex 4. Find the maximum or minimum of each quadratic function. a) f(x) = x 2 + 4x b) g(x) = –2x 2 + 4x – 5

13. Class Work Find the maximum or minimum value of each quadratic function. 4.f(x) = x 2 + 8x 5. g(x) = –4x 2 + 8x – 2

14. HW #6 p200 1,4,5,8,10,13,14,19,22,25,26, 29,32,34,39,59,61,62