Question

a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola

Answer 1

The vertex form of the equation is
`y = -(1)/(3)( x-1)^(2) +1`.

Explanation:

You will use the equation
`y=a(x-h)^(2) +k` to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get
`y= a(x - 1)^(2) +1`.

Then, we substitute the point as our x and y to get
`-2 = 9a+1` (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the
`9a` to get
`9a = 3`. Finally, divide by 9 on both sides to get
`a=(1)/(3)`.

Now, substitute your
`a` back into the equation to get y =
`-(1)/(3)(x-1)^(2)+1`.

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get
`y = -(1)/(3) x^(2) +(2)/(3) x+(2)/(3)`.