Answer:
[tex]f(x) = -2(x - 2)^2 + 1[/tex]
Step-by-step explanation:
Given the vertex, (2, 1) and point (3, -1):
We can plug in those values into the Vertex Form:
[tex]f(x) = a(x - h)^2 + k[/tex]
[tex]f(x) = a(x - 2)^2 + 1[/tex]
Plug in the other point, (3, -1) into the equation to solve for a:
[tex]-1 = a(3 - 2)^2 + 1[/tex]
[tex]-1 = a(1)^2 + 1[/tex]
-1 = a1 + 1
Subtract 1 from both sides of the equation to solve for a:
-1 - 1 = 1a + 1 - 1
-2 = 1a
[tex]\frac{-2}{1} = \frac{1a}{1}[/tex]
-2 = a
Therefore, the equation of the parabola in Vertex Form is:
[tex]f(x) = -2(x - 2)^2 + 1[/tex]
where a = -2, and the vertex, (2, 1) as its maximum point.
