100points will give brainlest g(x)=-2x^2+8x+3 write the function g(x) in the form y=a(x-h)^2+k. write the equation for the line of symmetry for the graph of g(x). show all your work and explain your 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

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.