Quadratic Equation

[xxxx]

1) A small object is thrown vertically up, 20 m from the surface of a planet, reaching a maximum of 36 m high, 2 s into its flight.
a) Write the equation relating the object’s height (y) to time (t), in the vertex form: ? = ?(? − ℎ)² + ?.
b) Convert the equation to the standard form, ? = ??² + ?? + ?.
c)Convert the equation to the factored form, ? = ?(? − ?)(? − ?).
d) Using the factored form, answer: when did the object hit the ground? Explain your answer.
e) Get the same answer from the standard form, using the quadratic (Bhaskara) formula.
f) Get (??, ?? ) from the factored form
g) Get (??, ??) from the formulas: ?? = − ? 2? and ?? = − ∆ 4? .

 

[Deleted member 4993]

1) A small object is thrown vertically up, 20 m from the surface of a planet, reaching a maximum of 36 m high, 2 s into its flight.
a) Write the equation relating the object’s height (y) to time (t), in the vertex form: ? = ?(? − ℎ) 2 + ?.
b) Convert the equation to the standard form, ? = ?? 2 + ?? + ?.
c)Convert the equation to the factored form, ? = ?(? − ?)(? − ?).
d) Using the factored form, answer: when did the object hit the ground? Explain your answer.
e) Get the same answer from the standard form, using the quadratic (Bhaskara) formula.
f) Get (??, ?? ) from the factored form
g) Get (??, ??) from the formulas: ?? = − ? 2? and ?? = − ∆ 4? .

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[HallsofIvy]

1) A small object is thrown vertically up, 20 m from the surface of a planet, reaching a maximum of 36 m high, 2 s into its flight.
a) Write the equation relating the object’s height (y) to time (t), in the vertex form: ? = ?(? − ℎ)² + ?.

What do YOU know about this? Do you know, for example, that a square is never negative? And, from that, that if "a" is positive this would be a parabola opening upward so that there was NO maximum- that tells you that a is negative. Then it is always "k minus something" so k is that maximum height, 36 m, and that the object reaches that maximum height when t- h= 0, at t= 2. So what is "h"?

b) Convert the equation to the standard form, ? = ??² + ?? + ?.

Do you know how to multiply a(t- h)^2?

c)Convert the equation to the factored form, ? = ?(? − ?)(? − ?).

So- factor!

d) Using the factored form, answer: when did the object hit the ground? Explain your answer.

ab= 0 if and only if one of a or b is 0. (x- a)(x- b)= 0 if and only if x= a or x= b.

e) Get the same answer from the standard form, using the quadratic (Bhaskara) formula.

The quadratic formula: ax^2+ bx+ c= 0 if and only if \(\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}\).

f) Get (??, ?? ) from the factored form
g) Get (??, ??) from the formulas: ?? = − ? 2? and ?? = − ∆ 4? .

??There was no "V" in the statement of the probem. Was there some other information you did not include?