Question

The graph shows g(x), which is a translation of f(x)=x^2. Write the function rule for g(x).
The graph shows a curved line that has a y-intercept at -8, as well as distinct points of (1, 3) and (-3, 1).
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers or simplified fractions.
FRACTIONS CANT BE USED! ! !

Answer 1

Because the three points (0, −8), (1, 3) and (−3, 1) force a vertical stretch, the vertex-form parameters are fractional. The exact vertex form is

g(x) = (7/2) (x + 15/14)^2 − 673/56.

If you prefer no fractions inside the parentheses, an equivalent form is

2g(x) = 7x^2 + 15x − 16

(or g(x) = (7x^2 + 15x − 16)/2).

Note: it is not possible to write a(x−h)^2 + k with all of a, h, k integers for these three given points.