SOLUTION: Graph the quadratic function. Indicate the vertex coordinates, the axis of symmetry line, the y-intercept, and x-intercepts. y=2x^2-4x+1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Graph the quadratic function. Indicate the vertex coordinates, the axis of symmetry line, the y-intercept, and x-intercepts. y=2x^2-4x+1      Log On


   

Question 417924: Graph the quadratic function. Indicate the vertex coordinates, the axis of symmetry line, the y-intercept, and x-intercepts.
y=2x^2-4x+1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

y=2x^2-4x+1  |y-intercept Pt(0,1) 

x-intercept when y = 0

2x^2-4x+1 = 0

 x+=+%284+%2B-+sqrt%288%29%29%2F%284%29+=+1+%2B-+sqrt%282%29%2F2 = 1 ± .707

Pt(.3,0) and Pt(1.7,0) the x-intercepts (rounded to nearest tenth)

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

y=2x^2-4x+1      |completing square to put into the vertex form

y= 2(x-1)^2 -2 +1 

y= 2(x-1)^2 -1   Vertex is Pt(1,-1) axis of symmetry is x = 1