Question

How is the graph of `g(x)=x^2+7` related to the graph of `f(x)=x^2`?

Answer 1

F(x) on a graph would be 7 units higher than g(x).

Explanation:

In an quadratic equation like `y = ax^2 + bx + c`, c is the y-intercept. (c moves the parabola up or down.) So, in your g(x), c=7, so 7 is the y-intercept, and in your f(x), c=0, so your y-intercept is 0. They have the same a (1) and b (0) (which moves it left or right), so they're identical except for their y-intercept.

You could also look at it like this: g(x) is basically the same thing as f(x) except for the +7, so g(x) is f(x) +7, so any point in the graph of g(x) will be 7 units above the point with the same x in the graph of f(x).