1. Quadratic Functions Lesson 3.3

2. Quadratic Function  Degree 2  Parabola shaped  Can open upward or downward  Always has a vertex which is either the max or min  Always has exactly one y-intercept  Can have 0, 1, or 2 x-intercepts  Is symmetric about a line through the vertex called the axis of symmetry

3. Forms of Quadratic Function  Transformation form: f(x) = a(x – h) 2 + k f(x) = a(x – h) 2 + k  Polynomial form: f(x) = ax 2 + bx + c f(x) = ax 2 + bx + c  x-Intercept form: f(x) = a(x – s)(x – t) f(x) = a(x – s)(x – t)  If a is positive, the graph opens upward

4. Transformation {f(x) = a(x – h) 2 + k}  Vertex  (h, k)  x-Intercepts   y-intercept  ah 2 + k

5. Polynomial {f(x) = ax 2 + bx + c}

6. x-intercept {f(x) = a(x – s)(x – t)}

7. Changing to Polynomial and x-intercept form  F(x) = 0.4(x – 3) 2 + 2 .4(x 2 – 6x + 9) + 2 .4(x 2 – 6x + 9) + 2.4x 2 – 2.4x + 5.6 {Polynomial}.4x 2 – 2.4x + 5.6 {Polynomial} b 2 – 4ac = -3.2 so there are no b 2 – 4ac = -3.2 so there are no x-intercepts x-intercepts  g(x) = 3x 2 – 3.9x – 43.2  3(x 2 – 1.3x – 14.4)  3(x 2 – 1.3x – 14.4) Quadratic formula step Quadratic formula step 3(x – 4.5)(x + 3.2) 3(x – 4.5)(x + 3.2)

8. Changing to Transformation Form  f(x) = -3x 2 + 4x – 1  g(x) = 0.3(x -2)(x + 1)  Lets look at pg. 168-169 for the work that is done  There is also quite a lovely summary of the previous 7 slides on page 169!

9. Application Example  The owner of a concession stand can sell 150 lunches per day at a price of #3 each. The cost to the owner is $2.25 per lunch. Each $0.25 price increase decreases sales by 30 lunches per day. What price should be charged to maximize profit?