Building Quadratic Fcns: marshmallow is launched straight up w/ slingshot

[Rinso]

A small marshmallow is launched straight up in the air with a slingshot. Its height h in meters, relative to te ground, is given by the function h(t) = 5 + 20 - 5t^2, where t is measured in seconds. About when does the marshmallow reach its maximum height?

 

[tkhunny]

A small marshmallow is launched straight up in the air with a slingshot. Its height h in meters, relative to te ground, is given by the function h(t) = 5 + 20 - 5t^2, where t is measured in seconds. About when does the marshmallow reach its maximum height?

I believe you are missing a "t" next to your "20".

You are expected to know some things about "quadratic functions". What do thy look like? Is here "maximum height" that you track down? How might you go about it?

 

[mmm4444bot]

They're asking for the t-coordinate of the parabola's vertex. (The y-coordinate gives the maximum height, and the t-coordinate tells you when the marshmallow gets there.)

If you have not yet learned meaning for either of the words 'parabola' or 'vertex', let us know.

Otherwise, there is a formula for finding the t-coordinate of the vertex.

Given: y = A∙t^2 + B∙t + C

t-coordinate of vertex = -B/(2A)

 

[HallsofIvy]

A small marshmallow is launched straight up in the air with a slingshot. Its height h in meters, relative to te ground, is given by the function h(t) = 5 + 20 - 5t^2, where t is measured in seconds. About when does the marshmallow reach its maximum height?

\(\displaystyle h(t)= 5+ 20t- 5t^2= 5+ 5(4t- t^2)\)

COMPLETE THE SQUARE! \(\displaystyle 4t- t^2= 4- 4+ 4t- t^2= 4- (t- 2)^2\)
Since that is 4 minus a non-zero number, it will be maximum when that number is 0: when t- 2= 0