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

_____

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

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a