Question

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

Answer 1

hello

Answer 2

hi

Answer 3

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

Answer 4

where you get -12/-4=3?

Answer 5

you their?

Answer 6

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

Answer 7

you did the whole problem their?

Answer 8

you did the whole problem their?

Answer 9

you did the whole problem their?

Answer 10

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)

Answer 11

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)

Answer 12

that looks odd lol

Answer 13

16/2 = 8 lol i forgot how to divide by 2 :)

Answer 14

-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

Answer 15

my mistake was thinking I could combine -y/2 and -15/2 .... silly me

Answer 16

(-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 ...