Question

Given the graph, find an equation for the parabola.

Answer 1

`\Large \boxed{\sf \bf \ \ y=(1)/(16)(a-3)^2-2 \ \ }`

Explanation:

Hello, please consider the following.

When the parabola equation is like

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

The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))

As the vertex is (3,-2) we can say that h = 3 and k = -2.

We need to find a.

The focus is (3,2) so we can say.

`2=-2+(1)/(4a)\\\\\text{*** We add 2. ***}\\\\(1)/(4a)=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=(1)/(16)`

So an equation for the parabola is.

`\large \boxed{\sf y=(1)/(16)(a-3)^2-2 }`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you