Question

A person standing at a ridge in the Grand Canyon throws a penny upward and toward the pit of the canyon. The height of the penny is given by the function h(t)=-12t^2+80t
What is the maximum height of the penny?

Answer 1

are you using calculus, or algebra to solve this?

Answer 2

algebra

Answer 3

in general, you can find the maximum x value of an quadratic equation like this.\[ax^{2} + bx + c = 0\]

let x = -b/(2a), this is the x-coordinate of the vertex (where a min/max value will be found)

in our case, we have \[-12t^{2} + 80t + 0 = 0\]

can you determine the x-coordinate (the t-coordinate in our case) of the vertex ?

Answer 4

I am very confused

Answer 5

try rewriting the quadratic in vertex form. then it will become clearer

Answer 6

what is the vertex form?

Answer 7

http://www.purplemath.com/modules/sqrvertx.htm

Answer 8

if you take my word that the x-coordinate of the vertex is always -b/(2a), then you'll agree that the x-coordinate of the vertex for our problem is -(80) / (2 * -12) = 10/3

let x = 10/3, solve for y
in other words
let t = 10/3, solve for h

Answer 9

so is my answer 133 1/3 feet

Answer 10

How many seconds will it take the penny to hit the ground?

Answer 11

at what height, h, is the ground? (this is a conceptual question)

Answer 12

It is the second part of the last question. The given function is h(t)=12t^2 +80t. And the maximum height of the penny, I believe, is 133 1/3 feet.

Answer 13

what is the value of h at ground level? think about this conceptually. how high is the ground ?

Answer 14

I don't know. I am terrible at word problems. I can never figure out how to put them together.