I honestly forgot how to to this so I had to refresh my memory with this website.
http://www.purplemath.com/modules/fromzero.htm
I'm sure it can explain how to do these better than I can. :)
1.
y = a[x - (1+√2)][x - (1 - √2)]
y = a[x - 1 - √2][x- 1 + √2]
y = a(x2 - x + √2(x) - x + 1 - √2 - √2(x) + √2 - 2)
y = a(x2 - 2x - 1)
Since the y-intercept is -4, x is 0 when y is -4. Use this information to find a.
-4 = a(02 - 2(0) - 1)
-4 = a(-1)
4 = a
So
y = 4(x2 - 2x - 1)
y = 4x2 - 8x - 4
Or you could say:
f(x) = 4x2 - 8x - 4
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2.
The zeros are at x = 2 and x = 4.
y = a(x-2)(x-4)
y = a(x2 - 6x + 8)
y is -2 when x is 3
-2 = a(32 - 6(3) + 8)
-2 = a(9 - 18 + 8)
-2 = a(-1)
2 = a
So
y = 2(x2 - 6x + 8)
y = 2x2 - 12x + 16
Or you could say:
f(x) = 2x2 - 12x + 16