Consider the function y=-3x^2+5x-2. Use completion of squares to write in standard form y=a(x-xv)^2+yv?

Question

Consider the quadratic function y = - 3x^2 + 5x - 2.
Use the completion of squares to write the function in the standard form y = a(x-xv)^2 + yv
(the v's are supposed to be subscript)

Answer 1

y=-3x^2+5x-2 factor out -3

y=-3(x^2-5/3x+2/3) complete the square

y=-3(x^2-5/3x+25/36-25/36+2/3) put in a(x-xv)^2 form

y=-3((x-5/6)^2-25/36+2/3) distribute -3 to the other two numbers

y=-3(x-5/6)^2+75/36-72/36 add like terms and simplify

y=-3(x-5/6)^2+1/12

Answer 2

common kind is Ax + via = C. So subtract 3/5x from the two components to get y-3/5x = -2 Rearrange so x is first. -3/5x + y = -2 Multiply each and everything via 5 to do away with 5 interior the denominator. -3x + 5y = -10 Then multiply eveything via -one million 3x - 5y = 10

Answer 3

-3(x-5/6)^2 +1/12
Hope this helps!!

Answer 4

y=-3(x^2-5/3x+2/3)
-3[(x-5/6)^2-1/6] is your answer