Answer:
y = -2(x -2)^2 + 11
Step-by-step explanation:
It works well to factor the leading coefficient from the first two terms.
... y = -2(x^2 -4x) +3
Now we want to add the square of half the x-coefficient inside parentheses, and subtract the equivalent quantity outside parentheses.
... y = -2(x^2 -4x +4) +3 - (-2·4)
... y = -2(x -2)^2 +11 . . . . . . . . simplify
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The form given in the problem statement is called "vertex form," where the vertex of the parabola is (h, k). A graph shows us the vertex is (2, 11), so we can write the function immediately as ...
... y = -2(x -2)^2 +11
