Answer:
[tex]y=-1(x-2)^2+1[/tex]
Step-by-step explanation:
The parabola has the vertex (2, 1) and goes through the point (4, -3).
We will use the vertex form, given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
Line 1)
So, by substitution:
[tex]\text{Vertex}=(h,k)=(2,1)\Rightarrow y=a(x-2)^2+1[/tex]
Lines 2-4)
Since (4, -3) is a point, y = -3 when x = 4:
[tex]-3=a(4-2)^2+1[/tex]
[tex]-3=a(2)^2+1[/tex]
[tex]-4=4a\Rightarrow a = -1[/tex]
Line 5)
By substitution, we acquire our equation*:
[tex]y=-1(x-2)^2+1[/tex]
