Question

The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x).
The graph shows a curved line that has no y-intercept, though the point does hit at (9,0). Distinct points are (7, 4) and (6, 9) -- only one side of the curved line is shown, the rest goes off-screen.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers or simplified fractions.

Answer 1

g(x) = (x - 9)^2

Work: assume g(x) = (x - h)^2 + k. From (9,0): k = 0. From (7,4): (7 - h)^2 = 4 → (7 - h) = ±2. Using (6,9) gives (6 - h)^2 = 9 → (6 - h) = ±3. Solving consistently gives h = 9, so g(x) = (x - 9)^2.