SOLUTION: how exactly do i get orderded pairs for the eguation it was an equation y=-x2+3x+3 then i the farthest i gotten on my formula is -3+- the square root of 21 divided by -2

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Question 87904: how exactly do i get orderded pairs for the eguation it was an equation y=-x2+3x+3 then i the farthest i gotten on my formula is -3+- the square root of 21 divided by -2
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(14933) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:
Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general form of the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -x%5E2%2B3%2Ax%2B3=0 (notice a=-1, b=3, and c=3)

x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A-1%2A3+%29%29%2F%282%2A-1%29 Plug in a=-1, b=3, and c=3



x+=+%28-3+%2B-+sqrt%28+9-4%2A-1%2A3+%29%29%2F%282%2A-1%29 Square 3 to get 9



x+=+%28-3+%2B-+sqrt%28+9%2B12+%29%29%2F%282%2A-1%29 Multiply -4%2A3%2A-1 to get 12



x+=+%28-3+%2B-+sqrt%28+21+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-3+%2B-+sqrt%2821%29%29%2F%282%2A-1%29 Simplify the square root



x+=+%28-3+%2B-+sqrt%2821%29%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

x+=+%28-3+%2B+sqrt%2821%29%29%2F-2 or x+=+%28-3+-+sqrt%2821%29%29%2F-2


Which approximate to

x=-0.79128784747792 or x=3.79128784747792


So our solutions are:
x=-0.79128784747792 or x=3.79128784747792

Notice when we graph -x%5E2%2B3%2Ax%2B3 we get:

+graph%28+500%2C+500%2C+-10.7912878474779%2C+13.7912878474779%2C+-10.7912878474779%2C+13.7912878474779%2C-1%2Ax%5E2%2B3%2Ax%2B3%29+

when we use the root finder feature on a calculator, we find that x=-0.79128784747792 and x=3.79128784747792.So this verifies our answer

Answer by stanbon(29603) About Me  (Show Source):
You can put this solution on YOUR website!
how exactly do i get ordered pairs for the eguation
it was an equation y=-x^2+3x+3 then i the farthest i gotten on my formula is -3+- the square root of 21 divided by -2
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It looks like you were trying to apply the quadratic formula. But
that is not the easiest way to find ordered pairs.
-----------
Getting ordered Pairs:
1st: pick a value for "x".
2nd: substitute that value of x into the equation to find the corresponding
value for y.
----------
For example:
If x=0, y= -0^2+4*0+3 = 3, giving you the ordered pair (0,3)
If x=1, y= -1^2+4*1+3 = 6, giving you the ordered pair (1,6)
etc.
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Cheers,
Stan H.