SOLUTION: I have a test tomorrow and i need to understand how to work complicated word problems on Quadratic functions. Here it is... Scouts used a slingshot to launch a small rock upward fr

Question 27379: I have a test tomorrow and i need to understand how to work complicated word problems on Quadratic functions. Here it is... Scouts used a slingshot to launch a small rock upward from a cliff 250 feet above a river. The initial velocity was 320 feet per second. The formula h=250+320t-16t^2 gives the height in feet h of the rock relative to the river after t seconds. A) What is the maximum height reached by the rock? B) After how many seconds did the rock reach its maximum height? C) After how many seconds did the rock strike the river?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
height=-16t^2+320t+250
This is a quadratic with a=-16, b=320, and c=250
a) The high point or "maximum" is at time t=-b/2a
t=-320/-32 = 10 seconds
Plug that time into the height formula to find the height
at t=10 seconds
h(10)=-16(10^2)+320(10)+250
= -160+320+250
= +160+250
= 410 feet
b) The rock will strike the ground when its height is zero.
So put "0" in place of height and solve for "t"
0=-16t^2+320t+250

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=118400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.752906583803284, 20.7529065838033. Here's your graph:

Cheers,
stan H.
RELATED QUESTIONS
I have a test tomorrow on Trigonometric Functions and I dont know how to do any of the... (answered by solver91311)

I need some help, I have a test tomorrow and I don't understand some of it. It's over... (answered by stanbon)

What is the main thing I need to remember when I am solving equation problems. I have a... (answered by jim_thompson5910)

How can you show vertical reflection, shift left 3, and shift up 6 to these functions:... (answered by nerdybill)

Hey I have a test tomorrow & I don't understand how to solve for... (answered by wilft1)

hey I'm Hailey and I don't really understand how to solve distributive propert problems.... (answered by srinivas123)

I don't know how to sove these problems. My teacher is horrible and explains nothing. I (answered by ankor@dixie-net.com)

Need help putting word problem into an equation. I have a quiz and test tomorrow and my... (answered by ikleyn)

Hey, I have a math test tomorrow and I honestly don't understand anything about Quadratic (answered by Alan3354,psbhowmick)