Warmup Homework Answers Homework Answers Part 2 4

Warm-up

Homework Answers

Homework Answers Part 2

4. 6 The Quadratic Formula and the Discriminant

Discriminant: 2 b – 4 ac determines how many and what type of solutions a quadratic has.

Examples: Determine the number and type of solutions the quadratic has. 1. x 2 – 6 x + 10 = 0

Steps to solve with the quadratic equation 1. 2. 3. Put the equation into standard form Identify a, b, and c Substitute into the quadratic equation and simplify

Examples: 3. 4 x 2 + 8 x = x 2 + 35

4. -2 x 2 = -2 x +3

Example 6

Example 7 A ball is thrown downward from a height of 6 feet with an initial velocity of 32 ft/sec. If the ball is caught at a height of 2 feet, for how long is the ball in the air?

Concept Summary: Solving Quadratic Equations Method Graphing Factoring Square Root Property Completing the Square Quadratic Formula Can be Used When to use it…

Homework Problems Page 270: 21 -29, 43

Homework Answers Question # a b 21 33 2 irrational 22 4 2 rational 23 49 2 rational 24 121 2 rational 25 -87 2 Complex 26 -40 2 Complex 27 36 2 rational 28 0 1 rational 29 1 2 rational c . 5, 1 3

Vertical Motion Model

Vertical Motion Model h = -16 t 2 + vot + ho h = ending height (feet) t = time (seconds) vo = initial velocity (feet per second) ho = initial height (feet)

Example 8 If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of one side of the square.

Example 9 A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d = -16 t 2 – 4 t + 382. How long after the rock is thrown is it 370 feet from the ground?

Exit slip time

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