SOLUTION: Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?       Log On


   

Question 115511: Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Remember, if an equation is in vertex form y=%28x-h%29%5E2%2Bk, then we know the vertex is (h,k)
Since we can see that the vertex is (-6,0), this means h=-6 and k=0

y=%28x-h%29%5E2%2Bk Start with the general equation in vertex form. In this case, a=1

y=%28x-%28-6%29%29%5E2%2B0 Plug in h=-6 and k=0.


y=%28x%2B6%29%5E2%2B0 Rewrite x-%28-6%29 as x%2B6.


y=%28x%2B6%29%5E2 Remove the zero term.


So the equation of the parabola that has been shifted 6 units to the left is y=%28x%2B6%29%5E2