SOLUTION: let F(x)=(x^2)-2x+3. find the axis of symmetry, vertex, and the x and y intercepts if they exist. sketch the graph of f.

Algebra ->  Graphs -> SOLUTION: let F(x)=(x^2)-2x+3. find the axis of symmetry, vertex, and the x and y intercepts if they exist. sketch the graph of f.      Log On


   

Question 43912: let F(x)=(x^2)-2x+3. find the axis of symmetry, vertex, and the x and y intercepts if they exist. sketch the graph of f.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
F(x) = x^2 - 2x + 3
Vertex:((-b/2a),f(x)) ---> (1,2)
Since this parabola will be vertical, the axis of symmetry will be equal to the value of the x-value.
Axis of Symmetry: x+=+1
x-intercept:
0+=+x%5E2+-+2x+%2B+3
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%282+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A1%2A3+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%282%29+
x+=+1+%2B-+i%2Asqrt%28+2+%29+ No real x-intercepts.
y-intercept:
y+=+0%5E2+-+2%2A0+%2B+3
y+=+3
graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+2x+%2B+3+%29+