SOLUTION: Find the minimum value of the quadratic y = 2x^2 - 8x + 10 by completing the square. Graph the resulting parabola. Thank you.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the minimum value of the quadratic y = 2x^2 - 8x + 10 by completing the square. Graph the resulting parabola. Thank you.       Log On


   

Question 1188446: Find the minimum value of the quadratic y = 2x^2 - 8x + 10 by completing the square. Graph the resulting parabola. Thank you.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite as y=2(x^2-4x+5)
=2(x^2-2x+4)+2; be careful here as the "4" is preceded by a multiplier of 2, and the constant in the parentheses is therefore 8, and need 2 more outside the parentheses to recover the original equation.
=2(x-2)^2+2
The minimum point is therefore (2, 2), reverse the sign of h, leave the sign of k alone.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2-8x%2B10%29
x-value is -b/2a=8/4=2
y-value is therefore 8-16+10=2

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

On completing the square see the lesson
    - HOW TO complete the square - Learning by examples
in this site.