1. Quadratic Equations Definitions:
A quadratic equation is an equation of the form ax2 + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.
Zero-Product Property: AB = 0 if and only if A = 0 or B = 0 .

2. Ex 1: Solve by factoring.
Ex 2: Solve by completing the square.

3. Quadratic Formula:
where a ≠ 0.

4. Ex 3: Find the solutions using the quadratic
formula.

5. Discriminant (D = b2 - 4ac) - the value that
Discriminant (D = b2 - 4ac) - the value that determines the types of solutions in a quadratic equation.
If D > 0, then the equation has 2 distinct real solutions.
If D = 0, then the equation has 1 real solution (double root).
If D < 0, then the equation has no real solutions (2 imaginary solutions).

6. Ex 4: Find the number of real solutions using the
discriminant.

7. Quadratic equations can be used to model real life situations.
Ex 5: A rectangular building lot is 8 feet longer than it is wide and has an area of 2900 ft2. Find the dimensions of the lot.
w = 50 ft and l = 58 ft

8. Ex 6: A jet flew from New York to Los Angeles, a. distance of 4200 km
Ex 6: A jet flew from New York to Los Angeles, a distance of 4200 km. The speed for the return trip was 100km/hr faster than the outbound speed. If the total trip took 13 hours, what was the jet’s speed from New York to Los Angeles?
R = 600 kph

9. Ex 7: An object thrown or fired straight upward at
Ex 7: An object thrown or fired straight upward at an initial speed of v0 ft/s will reach a height of h feet after t seconds, where h and t are related by the formula h = – 16t2 + v0t. Suppose that a bullet is shot straight upward with an initial speed of 800 ft/s.
a. When does the bullet fall back to ground level?
b. What does it reach a height of 6400 ft?
c. When does it reach a height of 2 miles?
d. How high is the highest point the bullet reaches?

10. h = – 16t2 + v0t
Suppose that a bullet is shot straight upward with an initial speed of 800 ft/s.
a. When does the bullet fall back to ground level?
b. What does it reach a height of 6400 ft?
c. When does it reach a height of 2 miles?
d. How high is the highest point the bullet reaches?
t = 50 s
t = 10 s and t = 40 s
Never
h = 10,000 ft

11. Assignment #8: S 1.3: pg
#2,4,9,28,29,32,55,61,66,75,78,88,90,93