Answer:
C.
f(x) = 8*(x - 1)²
f(x) = 8x² - 16x + 8
Explanation:
vertex form:
f(x) = a*(x - h)² + k
where (h, k) is the vertex of the parabola
In this case, the vertex of the parabola is at (1, 0). Replacing this information into the equation we get:
f(x) = a*(x - 1)²
The parabola passes through point (2, 8). Replacing this information into the previous equation we get:
8 = a*(2 - 1)²
8 = a
Then, the final equation is:
f(x) = 8*(x - 1)²
Expanding the quadratic term and applying distributive property:
f(x) = 8*(x² - 2x + 1)
f(x) = 8x² - 16x + 8