SOLUTION: Please help me out with this one! I've been stuck on it for a while now. Please show all work. I would greatly appreciate any help. {{{y = -x^2 + 4x - 3}}} A)Find the equatio

Algebra ->  Graphs -> SOLUTION: Please help me out with this one! I've been stuck on it for a while now. Please show all work. I would greatly appreciate any help. {{{y = -x^2 + 4x - 3}}} A)Find the equatio      Log On


   

Question 37115: Please help me out with this one! I've been stuck on it for a while now. Please show all work. I would greatly appreciate any help.
y+=+-x%5E2+%2B+4x+-+3
A)Find the equation for the axis of symmetry.
B)Find the coordinates of the vertex.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+-x%5E2+%2B+4x+-+3
first find the roots, if any
-x%5E2+%2B+4x+-+3+=+0
multiply both sides by -1
x%5E2+-+4x+%2B+3+=+0
%28x+-+3%29%2A%28x+-+1%29+=+0
***note***
the above equation with the signs reversed is ONLY for finding
the roots - it is not for anything else - the actual equation is
the one you started with
****************
the roots are +3 and +1
those are the values for x that make the above true
the axis of sym will be in the middle of the roots
%28r1+%2B+r2%29+%2F+2+=+a
%283+%2B+1%29+%2F+2+=+%2B2
The equation of the axis of symmety is x = 2
The vertex is on the axis of symmetry, so
find what y is when x = 2
y+=+-%282%5E2%29+%2B+4%282%29+-+3
y+=+-4+%2B8+-+3
y+=+%2B1
So, the vertex is at (2,1)
+graph%28+300%2C+300%2C+-2%2C+5%2C+-5%2C+2%2C+-%28x%5E2%29+%2B4%2Ax+-3%29+