What kind of transformation converts the graph of f(x)=6(x+3)^2+7 into the of g(x)=6(x+3)^2+6

Question

Translation 1 unit up

Translation 1 unit down

Translation 1 unit right

Translation 1 unit left

Answer 1

Given f(x) = 6(x + 3)² + 7 and g(x) = 6(x + 3)² + 6 then we know that these are two parabolas (the graphs of quadratic equations).

The standard form of a parabola is y = a(x – h)² + k, with the vertex at the point (h, k).

The above equations are already in this form so we can say that f(x) has a vertex at (-3, 7) and g(x) has its vertex at (-3, 6).

Hence we can see that g(x) has been translated 1 unit DOWN from f(x).

You can use Desmos Graphing or similar to look at the graphs.