50 POINTS
1. A child launches a toy rocket from the top of a slide at the park. Suppose the equation
−162 + 28 + 8 = 0 can be used to find how many seconds it will take for the rocket to hit the ground.

a. Write the equation in factored form. [Hint: factor out a -4 first]

b. Use the zero product property to solve the equation. Show all the steps needed to find both answers.

c. Pick the logical answer. Why does the other answer not make sense? Explain how your solution relates to this situation. Put your answer into the sentence.

A) The equation in factored form is (4t + 1)(t - 2) = 0
B) The solutions of the equation are t = -1/4 and t = 2
C) It will take 2 seconds for the rocket to hit the ground
Step-by-step explanation:
* Lets study the information in the problem
- A child launches a toy rocket from the top of a slide
- The equation of the motion is -16² + 28t + 8 = 0, where t is the time
 of rocket to hit the ground
* Now lets solve the problem
- At first simplify the equation
∵ -16t² + 28t + 8 = 0
∵ Al the terms have a factor 4
- Divide all terms by 4
∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1
∴ 4t² - 7t - 2 = 0
- Lets factorize
∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket
∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket
∵ 4t + -2 = -8t ⇒ product of the extremes
∵ 1t × 1 = 1t ⇒ product of means
∵ -8t + 1t = -7t ⇒ middle term
∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)
∴ (4t + 1)(t - 2) = 0
A) The equation in factored form is (4t + 1)(t - 2) = 0
- Lets use the zero product property to solve the equation
∵ (4t + 1)(t - 2) = 0
- Equate each factor by 0
∵ 4t + 1 = 0 ⇒ subtract 1 from both sides
∴ 4t = -1 ⇒ divide both sides by 4
∴ t = -1/4
OR
∵ t - 2 = 0 ⇒ add 2 for both sides
∴ t = 2
B) The solutions of the equation are t = -1/4 and t = 2
C) We can not accept the answer t = -1/4 because there is no negative
    value for the time
∴ The answer is t = 2 only
* It will take 2 seconds for the rocket to hit the ground

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