Today in Pre-Calculus

1. Today in Pre-Calculus • Need calculator and textbook • Notes: • Quadratic Functions • Modeling • Go over test • Go over last night’s homework • Homework

2. Quadratic Functions Standard form: f(x) = ax2 + bx + c Roots (zeroes or x-intercepts) are found by factoring or using quadratic formula Vertex form: f(x) = a (x – h)2 +k Vertex of the parabola (h, k) Axis of symmetry: x = h

3. Quadratic Functions To convert from standard form to vertex form using algebra: Complete the square. Example: y = 2x2 + 16x + 31

4. Practice Example: Use algebra to describe y = 3x2 – 18x – 17 y = 3(x2 – 6x) – 17

5. Formulas for h and k Example: y = 2x2 + 16x + 31

6. Example Write the equation for a parabola with a vertex (-1,2) that goes through (6,100).

7. Vertical Free Fall Motion The height s and vertical velocity v of an object in free fall are given by s(t) = -½ gt2 + v0t + s0 and v(t) = -gt + v0 Where t is time (in seconds), g≈32 ft/sec2 ≈9.8m/sec2 is the acceleration due to gravity, v0 is the initial vertical velocity of the object, and so is its initial height.

8. Example Page 184: Number 61

9. Example Number 59

10. Homework • Pg. 182: 23,25,35,37,39,41,58,62,63