1 answer

How do you graph #y=-2(x-1)^2+1#?

Question:

How do you graph #y=-2(x-1)^2+1#?

Answers

With a vertex of #(1,1)#, use #x#-values of #-1,0,2,3# in the equation to determine reference points, creating the graph: graph{-2(x-1)^2+1 [-10, 10, -5, 5]}

Explanation:

Knowing the formula is #f(x)=a(x-h)^2+k#, you can determine that the vertex of the graph will be at point #(1,1)#, as these values translate the entire graph itself. The #a#-value being negative indicates that the vertex is a maximum, making the graph open downward with a vertical stretch factor of #2#. Depending on your teacher, you may be required to include more or fewer reference points in a graph, but the simplest rule is to plugin 2 #x#-values less than your initial point (being the vertex), and 2 #x#-values greater than your initial point to the function.

Following this concept, you should get additional points: #(-1,-7), (0,-1), (2,-1),# and#(3,-7)#. It is also helpful to realize that the points are a mirror of one another in their #y#-values, so long as the #x#-values are an equal distance from the #x#-value of the vertex.

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