You can
put this solution on YOUR website!i dont understand how to complete the square on y=.5x^2-3x+19/2. i also have to graph this parabola and i dont know how
:
It's easier to complete the square if the coefficient of x^2 is 1
Multiply equation by 2 to get that. I also gets rid of the fraction, you have:
x^2 - 6x + 19 = 0
We want to have the third term value make it a perfect square, so we:
x^2 - 6x + ___ = -19; subtracted 19 from both sides
:
Find the values of the third term, divide the coefficient of x by 2, and square:
6/2 = 3, square 3 and we have 9, we have to add 9 to both sides.
:
x^2 - 6x + 9 = -19 + 9; (x^2-6x+9 is a perfect square)
:
(x - 3)^2 = -10
:
Take the square root of both sides:
x - 3 = +/-
:
We can't have a neg square root, use i, the square root of -1
x - 3 = +/-
:
x = 3 +/-
; add 3 to both sides
:
The two solutions (this equation does not have any real roots)
x = 3 +
;
and
x = 3 -
;
:
;
To graph this, assign values to x and find y, a table of values would look like this:
x | Y
-------
-3 | 23
-2 | 17.5
-1 | 13
0 | 9.5
+1 | 7
+2 | 5.5
+3 | 5
+4 | 5.5
+5 | 7
+6 | 9.5
+7 | 13
You should be able to find +8 and +9, as you can see, it is a parabola
You can
put this solution on YOUR website!To find the roots, set
You first have to multiply both sides by
in
order to get rid of the
in front of the
term
The rule is, take 1/2 of the coefficient of the x-term, then
square it, then add the result to both sides
Now subtract
from both sides
Right away, I see that something squared is supposed
to be negative, so the "something", which is
,
must be an imaginary quantity
Take the square root of both sides
There are 2 answers,
and
check answer:
OK
