Question

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

Answer 1

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.