SOLUTION: Find the vertex, x and y intercepts of the parabola given by the equation y= 3x2-2x+1

Algebra ->  Linear-equations -> SOLUTION: Find the vertex, x and y intercepts of the parabola given by the equation y= 3x2-2x+1      Log On


   

Question 518220: Find the vertex, x and y intercepts of the parabola given by the equation
y= 3x2-2x+1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex is at +-b%2F%282a%29+
+a+=+3+
+b+=+-2+
+x%5Bv%5D+=+-b%2F%282a%29+
+-b%2F%282a%29+=+-%28-2%29%2F%282%2A3%29+
+-b%2F%282a%29+=+1%2F3+
+y%5Bv%5D+=+3%2A%281%2F3%29%5E2+-+2%2A%281%2F3%29+%2B+1+
+y%5Bv%5D+=+1%2F3+-+2%2F3+%2B+3%2F3+
+y%5Bv%5D+=+2%2F3+
The vertex is at ( 1/3, 2/3 )
----------------------
y-intercept:
+y+=+3x%5E2+-+2x+%2B+1+
+y+=+3%2A0+-+2%2A0+%2B+1+
( 0,1)
-------------------
x-intercept:
+3x%5E2+-+2x+%2B+1+=+0+
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-2+
+c+=+1+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29+
x+=+%28+2+%2B-+sqrt%28+4+-+12+%29%29+%2F+6+
+x+=+%28+2+%2B-+2%2Asqrt%282%29%2Ai+%29+%2F+6+
+x+=+%28+1+%2B-+sqrt%282%29%2Ai+%29+%2F+3+
There is no x-intercept, since both
roots are complx numbers
Here's a plot:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-2%2C+10%2C+3x%5E2+-+2x+%2B+1%29+