Quadratic Equations Definitions:

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Presentation transcript:

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 .

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

Quadratic Formula: where a ≠ 0.

Ex 3: Find the solutions using the quadratic formula.

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).

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

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

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

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?

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

Assignment #8: S 1.3: pg 105-107 #2,4,9,28,29,32,55,61,66,75,78,88,90,93