Question

Help with the Quadratic Equation! Will give medals for correct answer!

Answer 1

Where is the question : ^)

Answer 2

A ball is launched from a sling shot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

After 1 second, the ball is 121 feet in the air; after 2 seconds, it is 224 feet in the air.

Find the height, in feet, of the ball after 3 seconds in the air.

Answer 3

I don't understand how to do these. I don't understand the lesson and my teacher just tells me to look at the lesson. If you could explain how to do it, that'd be great, too

Answer 4

I got 327 for the height but I don't know.

Answer 5

I probably did it wrong : ^)

Answer 6

Yeah, it was incorrect :^(

Answer 7

r.i.p

Answer 8

My apologies.

Answer 9

It's okay.

Answer 10

Any quadratic equation can be put in the form \[y = ax^2 + bx + c\]where \(a,b,c\) are constants and \(a\ne0\)

We have two points, (\(1,121\)) and (\(2,224\)), where the x value is the time in seconds (the independent variable) and the y value is the height (the dependent variable). We can also assume a third point: (\(0,0\)) representing the state before the ball is launched

Plug all the points into the equation and you have 3 equations in 3 unknowns, which you can then solve to find the values of \(a,b,c\).

\((0,0)\):
\[0 = a(0)^2 + b(0) + c\]

\((1,121)\):
\[121 = a(1)^2 + b(1) + c\]

\((2,224)\):
\[224 = a(2)^2 + b(2) + c\]

I think you will find the value of \(c\) quite easy to determine :-)

When you have found \(a\) and \(b\), use them (along with \(c\)) to fill out your quadratic formula, then evaluate it at \(x=3\) for the answer. You should find that your answer starts with a 3.