The functions f(x) = −(x − 1)2 + 5 and g(x) = (x + 2)2 − 3 have been rewritten using the completing-the-square method. apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

The vertex form of a quadratic function:

(h,k) - the coordinates of the vertex

If a>0, then the parabola opens upwards, so the vertex is the minimum of the function.

If a<0, then the parabola opens downwards, so the vertex is the maximum of the function.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

answer: y=4000x+14000

step-by-step explanation: