Answer:
[tex]f(x)=-7(x-3)^2+1[/tex]
Step-by-step explanation:
Vertex form of a quadratic is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
We are given that the vertex is (3, 1). Hence, h = 3 and k = 1. By substitution:
[tex]f(x)=a(x-3)^2+1[/tex]
We are also given a point (2, -6). This means that when x = 2, f(x) = -6. Hence:
[tex]-6=a((2)-3)^2+1[/tex]
Solve for a. Subtract:
[tex]-6=a(-1)^2+1[/tex]
Simplify:
[tex]-6=a+1[/tex]
Therefore:
[tex]a=-7[/tex]
Hence, our quadratic is:
[tex]f(x) = -7 (x-3)^2 + 1[/tex]
