We have vertex form for parabola equation as
[tex] Y = a(X-h)^2 + k [/tex]
where (h,k) is the vertex.
As the turning point given here is (2,1) so thats the vertex.
On comparing (2,1) with (h,k), we can see
h = 2, k = 1
Plugging 2 in h place and 1 in k place in
[tex] Y = a(X-h)^2 + k [/tex] we get
[tex] Y =a(X-2)^2 + 1 [/tex] ------------------------ (1)
Now we need to find value of a.
For that we will use point (0,5) given on parabola.
On comparing (0,5) with point (X,Y) we get X = 0, Y = 5
so plug 0 in X place and 5 in Y place in equation (1)
[tex] Y = a(X-2)^2 + 1 [/tex]
[tex] 5 = a(0 -2)^2 + 1 [/tex]
Simplify and solve for a as shown
[tex] 5 = a(-2)^2 + 1 [/tex]
[tex] 5 = a(4) + 1 [/tex]
5 -1 = a(4) + 1 - 1
4 = a(4)
[tex] \frac{4}{4} = \frac{a(4)}{4} [/tex]
1 = a
Now plug 1 in a place in equation (1) as shown
[tex] Y = 1(X-2)^2 + 1 [/tex]
[tex] Y = (X-2)^2 + 1 [/tex]
So thats the vertex equation of parabola and final answer.
Answer:
The correct answer is A, "y = (x - 2)² + 1."
Step-by-step explanation:
I just completed the test and got it right.
