SOLUTION: How do you find the vertex, axis of symmetry and graph: f(x) -x^2-6x+3, in the back of my math book it says the vertex is (-3,12) i keep getting (-3,-6) Thanx :)

Algebra ->  Graphs -> SOLUTION: How do you find the vertex, axis of symmetry and graph: f(x) -x^2-6x+3, in the back of my math book it says the vertex is (-3,12) i keep getting (-3,-6) Thanx :)      Log On


   

Question 145727: How do you find the vertex, axis of symmetry and graph: f(x) -x^2-6x+3, in the back of my math book it says the vertex is (-3,12) i keep getting (-3,-6) Thanx :)
Found 3 solutions by stanbon, jim_thompson5910, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the vertex, axis of symmetry and graph: f(x)= -x^2-6x+3, in the back of my math book it says the vertex is (-3,12) i keep getting (-3,-6)
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Vertex occurs where x = -b/2a = 6/-2 = -3
f(-3) = -(-3)^2-6(-3)+3 = -9+18+3 = 12
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Vertex at (-3,12)
Axis at x = -3
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graph%28400%2C300%2C-10%2C10%2C-10%2C20%2C-x%5E2-6x%2B3%29
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-x%5E2-6x%2B3 Start with the given function


f%28-3%29=-%28-3%29%5E2-6%28-3%29%2B3 Plug in x=-3 (which is the x-coordinate of the vertex)


f%28-3%29=-9-6%2A-3%2B3 Raise -3 to the 2nd power to get 9


f%28-3%29=-9--18%2B3 Multiply 6 and -3 to get -18


f%28-3%29=-9%2B18%2B3 Rewrite -9--18%2B3 as -9%2B18%2B3


f%28-3%29=9%2B3 Add -9 and 18 to get 9


f%28-3%29=12 Add 9 and 3 to get 12


So when x=-3, we have y=12


This means that the vertex is (-3,12)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex and axis of symmetry:
f%28x%29+=+-x%5E2-6x%2B3
The equation of the axis of symmetry is:
x+=+-b%2F2a
x+=+-%28-6%29%2F2%28-1%29
x+=+6%2F%28-2%29
x+=+-3 Substitute this into the given function to find the vertex location.
f%28-3%29+=+-%28-3%29%5E2-6%28-3%29%2B3
f%28-3%29+=+-9%2B18%2B3
f%28-3%29+=+12
The vertex is at: (-3, 12)
graph%28400%2C400%2C-10%2C5%2C-5%2C15%2C-x%5E2-6x%2B3%29