The equation of the function is:
[tex]y = 3(x - 4)^2 + 2[/tex]
Solution:
The vertex form of equation is given as:
[tex]y = a(x - h)^2 + k[/tex]
Where, (h, k) is the vertex
Given that, The graph of a quadratic function has the vertex (4, 2)
(h, k) = (4, 2)
Substitute in eqn
[tex]y = a(x - 4)^2 + 2[/tex]
And passes through the point (5,5)
Substitute (x, y) = (5, 5) in above
[tex]5 = a(5 - 4)^2 + 2\\\\5 = a + 2\\\\a = 3[/tex]
Substitute a = 3 and (h, k) = (4, 2) in vertex form
[tex]y = 3(x - 4)^2 + 2[/tex]
Thus the equation of function is found
