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

With a vertex of $\left(1 , 1\right)$, 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]}
Knowing the formula is $f \left(x\right) = a {\left(x - h\right)}^{2} + k$, you can determine that the vertex of the graph will be at point $\left(1 , 1\right)$, 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: $\left(- 1 , - 7\right) , \left(0 , - 1\right) , \left(2 , - 1\right) ,$ and$\left(3 , - 7\right)$. 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.