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Given the following function, F(x)=4x^2-16x+27, identify where the vertex would be?A. (-2,75)B. (-2,11)C.(2,11)D. (0,27)Need an explanation and answer!

User Jeremycg
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we have the equation f(x) = 4x^2 - 16x + 27

Using the completing the square nethod

4x^2 -16x + 27

firstly, make sure the coefficient of x^2 is 1

divide all through by 4

4x^2/4 -16x/4 + 27/4

x^2 - 4x + 27/4 = 0

x^2 - 4x = -27/4

make the linear expression a perfect square

x^2 -4x/2 = -27/4

x^2 -(2x)^2 = -27/4

add the perfect square to both sides

x^2 -(2x)^2 = -27/4 + 4

(x - 2)^2 = -27/4 + 4

solving the Left hand side of the equation

-27/4 + 4

lcm is 4

-27 + 16/4/4

-11/4

(x - 2)^2 = -11/4

The vertex would lie when x = -2 and y =11

(-2 , 11)

User Margie
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