Question

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

Answer 1

Answer:

The vertex form of the equation is $y = -\frac{1}{3}( x-1)^{2} +1$.

Step-by-step 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 $a=\frac{1}{3}$.

Now, substitute your $a$ back into the equation to get y = $-\frac{1}{3}(x-1)^{2}+1$.

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get $y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}$.