Question

Pre-cal 12 Question!




Writing a polynomial equation.


Determine the equation of the polynomial of the least degree that is symmetric to the y-axis, tangent to the x-axis at (3,0) and has P(0)=27.

Answer 1

Hmm ya! A quadratic should work! :)

We're given that:
P(0)=27
P(3)=0 (This point must also be the vertex if we're going to try and make a quadratic work)

So my thinking is...
Our vertex is at (3,0),
let's write a generic quadratic in vertex form,
and then use the other piece of information to solve for a, the amplitude!

Answer 2

ok

Answer 3

\[\large\rm P(x)=a(x-h)^2+k\]With vertex: \(\large\rm (h,k)\)
So our equation thus far should be,\[\large\rm P(x)=a(x-3)^2+0\]Something like that, ya?

Answer 4

exactly

Answer 5

so in yesterday lesson, I learne to find the value of a. making x=0 and plugging in the value of y for p(x), but the ansewr would be a=0

Answer 6

Confusing

Answer 7

Your coordinate point is like this:\[\large\rm (x,P(x))\quad= (0,27)\]So we replace x's with 0's,
and P(x) with 27,
ya?\[\large\rm P(x)=a(x-3)^2\]\[\large\rm 27=a(0-3)^2\]

Answer 8

We're calling it P(x), but it's really just y,
hopefully you can get comfortable with the function notation :)

Answer 9

yea value of a would be 3
a=3

Thus,

P(x)= 3(x-3)^2 + 0

Answer 10

Yay good job \c:/

And depending on whether not they want that in `standard form`,
you might want to expand out the square.

It doesn't look like the instructions were asking for that though.

Answer 11

@zepdrix sure,

I still have one question

Answer 12

k

Answer 13

Hmm hold on, did we screw something up...
"symmetric about the y-axis.. thinking

Answer 14

I do not understand what it means

Answer 15

I guess it means both sides should be equal, or look the same

Answer 16

symmetric about the y-axis means that it can be reflected across the y-axis and still be the same shape.Yes, like this example.
When reflected over, it covers itself up.