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# Given is the function f(x) = -x2

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Given is the function f(x) = -x2

a. The graph of f shifted 3 units down. The graph that comes into existence, belongs to the function g. Calculate the points of intersection of the graph of g with the line y = -28

b. The graph of h starts from the graph of f and has been shifted up a few unit. Then the graph is multiplied with the factor 2. The function notation for the new graph is h(x) = -2x2 + 6. Calculate how many units graph of f was shifted up to form the new graph.

Jun 10, 2019

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Given is the function f(x) = -x2

a. The graph of f shifted 3 units down. The graph that comes into existence, belongs to the function g. Calculate the points of intersection of the graph of g with the line y = -28

The new function is

g(x) =  -x^2 - 3        set this = to 28

-x^2 - 3  = -28       add 3 to both sides

-x^2  = - 25           multiply through by - 1

x^2  = 25              take both roots

x =  ±√25

x = ±5

So....the points of intersection  are   (5, -28)    and (-5, 28)

b. The graph of h starts from the graph of f and has been shifted up a few unit. Then the graph is multiplied with the factor 2. The function notation for the new graph is h(x) = -2x2 + 6. Calculate how many units graph of f was shifted up to form the new graph.

Let the sfift of f  be  c units

So we have that  f(x)  - -x^2 + c

2f(x)   =  2 [-x^2 + c ]  =  -2x^2 + 6

-2x^2 + 2c  = - 2x^2 + 6

So

2c  = 6

c = 3 units   Jun 10, 2019