Question

If the graph of the function f defined by

f(x)=-4x^2-3

is translated vertically upward by 7 units, it becomes the graph of a function g.

Find the expression for g(x).

Answer 1

A verticle shift would mean you add to your equation. So just add 7 since you're going up.
4x^2-3+7=4x^2+4

Answer 2

Answer: g(x) = 4x² + 4

Explanation:

Vertically translating a graph is one and the same as shifting the base graph (every plotted point in the graph) up or down in the direction of the y-axis. Any translation say "q" moves the graph upward when "q" is a postive value and downward when "q" is negative value.

Therefore, a graph of f(x) translated 7 units vertically is gotten by moving each point on the graph 7 units vertically upwards. And so,

Give that f(x) = 4x² - 3

And the function f(x) is translated vertically upwards by 7 units to give function g(x), it then means that:

g(x) = f(x) + 7

g(x) = 4x² - 3 + 7

g(x) = 4x² + 4