+96 Find the equation whose graph is a parabola with vertex $(2,4)$, vertical axis of symmetry, and contains the point $(1,1)$. Express your answer in the form "$ax^2+bx+c$".
+23252 Starting with this form: y - k = a(x - h)2 where (h, k) is the vertex.
---> y - 4 = a(x - 2)2
Now, the problem is to find the value of a.
Use the point (1, 1) ---> 1 - 4 = a(1 - 2)2 ---> -3 = a(-1)2 ---> -3 = a
So, the equation is: y - 4 = -3(x - 2)2
Multiply this out: y - 4 = -3(x2 - 4x + 4)
y - 4 = -3x2 + 12x - 12
y = -3x2 + 12x - 8
