Answer:
f(x) = -4x²+24x -28
Step-by-step explanation:
The given zeros are a sum and a difference. You can use the special factoring of the product of a sum and difference to simplify the product of the factors of the quadratic. Each zero 'p' corresponds to a factor (x -p):
f(x) = a(x -(3 +√2))(x -(3 -√2)) = a((x -3)² -(√2)²) = a((x -3)² -2)
We can find the leading coefficient 'a' from the given point:
f(1) = -8 = a((1 -3)² -2) = 2a
a = -8/2 = -4
Then the function can be written as ...
f(x) = -4((x -3)² -2) = -4(x² -6x +9 -2)
f(x) = -4x²+24x -28
