1. Identifying polynomial variables

Hi,

I hope someone can help. I'm trying to solve for the following problem:

So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:

I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.

- Olivia

2. Re: Identifying polynomial variables

$y=a(x-h)^2+k$

vertex at $(3,12)=(h,k)$

$y=a(x-3)^2+12$

$(0,1)$ is the y-intercept ...

$1=a(0-3)^2+12 \implies a=-\dfrac{11}{9}$

$y=-\dfrac{11}{9}(x-3)^2+12$

expand and collect like terms on the right side to determine the coefficients $b$ and $c$

3. Re: Identifying polynomial variables

Originally Posted by otownsend

So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:

I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.
You posted this as a calculus question.
So the derivative, $2ax+b=0)$ at $(3,12)$.