Find the vertex and all intercepts of the quadratic function f(x) = –2x2 + 12x – 15.I need to review for a test, plz help

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Find the vertex and all intercepts of the quadratic function f(x) = –2x2 + 12x – 15.I need to review for a test, plz help

Mathematics
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hello
hi
the vertex x compnent is -12/-4 = 3; use that value to determine the y component teh rest is either complete the square, or quadrtic formula it... you get the same results

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where you get -12/-4=3?
you their?
ok.... lets do it this way; we want the first# to be 1; so divide it all by -2: y = x^2 -6x +15/2 = 0 for simplicities sake x^2 -6x + ___ = -15/2 ; we subtracted 15/2; now we wanna complete the square on the left side we complete the square by making it a perfect square; so we need a number that when added to itself makes -6; then we can square that number to complete it :) x^2 -6x + ___ = -15/2 -3 + -3 = -6; -3(-3) = 9, lets use 9 to fill in the blank x^2 -6x +9 = -15/2 +9 ; we added 9 to each side, now convert the left side to its perfect square look, and add the rightside together like this: (x-3)^2 = 3/2 ; now sqrt both sides x-3 = +- sqrt(3/2) ; now add 3 to both sides to get x = 3 +- sqrt(3/2) ; and dbl chech to make sure I didnt mess it up lol
you did the whole problem their?
you did the whole problem their?
you did the whole problem their?
the first number there is the vertexes 'x' component; use it to find the 'y' component. the roots are simply what x =: x = 3 + sqrt(3/2) AND x = 3 - sqrt(3/2)
another way would be to solve it for the geometric interpretation of the equation; which is similar except we dont use =0, we use =y y = –2x2 + 12x – 15 (-1/2)y = x^2 -6x +15/2 (-1/2)y -15/2 = x^2 -6x -16y/2 +9 = x^2 -6x +9 -4y +9 = (x-3)^2 -4(y - 9/4) = (x-3)^2 vertex = (3, 9/4)
that looks odd lol
16/2 = 8 lol i forgot how to divide by 2 :)
-8y +9 = (x-3)^2 -8 (y - 9/8) = (x-3)^2; vertex = (3, 9/8) ?? lets check: –2(3)^2 + 12(3) – 15 = y -18 -15 +36 = y -33 + 36 = y 3 = y .... well, I got the x right lol
my mistake was thinking I could combine -y/2 and -15/2 .... silly me
(-1/2)y -15/2 +9 = x^2 -6x +9 (-1/2)y +3/2 = (x-3)^2 (-1/2) (y-3) = (x-3)^2 vertex = (3,3) that did it ...

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