The vertex formula:
[tex]f(x)=a(x-h)^2+k[/tex]
(h, k) - vertex
We have vertex (2, 3). Therefore:
[tex]f(x)=a(x-2)^2+3[/tex]
We know that the parabola passes (1, -7).
Put the coordinates of this point into the function equation
x = 1, f(x) = -7
[tex]a(1-2)^2+3=-7\ \ \ \ |-3\\\\a(-1)^2=-10\to a=-10[/tex]
Therefore we have:
[tex]f(x)=-10(x-2)^2+3[/tex]
Use [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]f(x)=-10(x^2-2x(2)+2^2)+3=-10(x^2-4x+4)+3\\\\=-10x^2+40x-40+3=-10x^2+40x-37[/tex]
Answer: f(x) = -10x² + 40x - 37
