The function f is defined as follows. f (x)=-5x²+4
If the graph of f is translated vertically upward by 3 units, it becomes the graph of a function h.
Find the expression for h (x).

The new expression   h(x) = 5 x² + 7

Step-by-step explanation:

Type of transformation                          change to co-ordinate point

a)  Vertical translation up 'd' units                  (x , y) → (x , y + d)

b) Vertical translation down 'd' units              (x , y) → (x , y - d)

c) Horizontal translation up 'c' units               (x , y) → (x+ c , y )

d) Horizontal translation down 'c' units          (x , y) → (x- c , y )

Given function  f (x)=-5x²+4

Vertical translation up '3' units then change to new function

            h(x) = 5 x² + 4 + 3

            h(x) = 5 x² + 7

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

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