SOLUTION: A) Let g(x) = x^2+bx+11. The point lies on (-1,8) on the graph of g. Find the value of b. b) The graph of f(x) = x^2 is transformed to obtain the graph of g. Describe this trans

Question 1193868: A) Let g(x) = x^2+bx+11. The point lies on (-1,8) on the graph of g. Find the value of b.
b) The graph of f(x) = x^2 is transformed to obtain the graph of g. Describe this transformation.
Answer by ikleyn(52879) (Show Source): You can put this solution on YOUR website!
.
A) Let g(x) = x^2+bx+11. The point lies on (-1,8) on the graph of g. Find the value of b.
b) The graph of f(x) = x^2 is transformed to obtain the graph of g. Describe this transformation.
~~~~~~~~~~~~~~~

(a)  To answer question  (a),  you should substitute  -1  instead of  x  in the formula and substitute   8  instead of  y.

     You will get then


         (-1)^2 + b(-1) + 11 = 8,

     or

         1      - b    + 11 = 8

         1      - 8    + 11 = b

                  4         = b.

     ANSWER.  b = 4.   The function  g(x)  is  g(x) = .




(b)  So, the function  g(x)  is  g(x) = .


     Complete the square and get  g(x) =  = .


     This formula says you that to get the plot of g(x), you should start
     
     from plot of function  y = ,  translate it 2 units left  and 7 units vertically up.

Solved.

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