Question

Write the quadratic variation equation for the relationship: y varies directly with x squared and y=18 when x=3

Answer 1

if \(a\) varies directly with \(b\), that means we can write \(a = kb\) where \(k\) is the constant of variation. Here you have \(y\) varies directly with \(x^2\), so we write\[y=kx^2\]

Now to find \(k\), simply plug in your known values of \(x = 3, y = 18\) and solve for \(k\).

Answer 2

do you have an answer for me to check?

Answer 3

I don't get itttttttttt

Answer 4

Okay, use your words, what don't you get? Do you not get how I came up with \(y = kx^2\), or how to find the value of \(k\)?

Answer 5

All of it

Answer 6

Okay, if you have <thing 1> varying directly with <thing 2>, that means that

<thing 1> = <a constant> * <thing 2>

That's direct variation. If <thing 2> goes up, <thing 1> goes up in proportion. If <thing 2> goes down, <thing 1> goes down, again in proportion.

Answer 7

So, here in this problem, we have <thing 1> is \(y\), and <thing 2> is \(x^2\). Therefore, the form of our equation will be\[y = kx^2\]Does that make sense now?

Answer 8

yeah

Answer 9

Okay, now we need to find the value of \(k\) when \(x = 3\) and \(y = 18\)

\[y = kx^2\]Plug in the values we know:\[18=k(3)^2\]Can you solve that for \(k\)?

Answer 10

k=2 ?

Answer 11

Yes, that's correct! So what is our final formula, if \(k=2\)?

Answer 12

Here's a graph of the resulting equation, with a grid line showing the point (3,18)

Answer 13

oh okay well thanks for the help