SOLUTION: Convert each quadratic function into vertex form. State the vertex, axis of symmetry, and direction of opening: 1. y = 2x^2-4x+3

Algebra ->  Rational-functions -> SOLUTION: Convert each quadratic function into vertex form. State the vertex, axis of symmetry, and direction of opening: 1. y = 2x^2-4x+3      Log On


   

Question 106966: Convert each quadratic function into vertex form. State the vertex, axis of symmetry, and direction of opening:
1. y = 2x^2-4x+3
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
general equation is y=a(x-h)^2+k

y=2(x^2-2x)+3 ... adding 1 inside the parentheses makes (x-1)^2
...but you can't just add to one side of an equation
...and adding 1 inside the parentheses is effectively adding 2, so 2 is also subtracted

y=2(x^2-2x+1)+3-2 ... y=2(x-1)^2+1

so the vertex is (1,1)

axis of symmetry goes through the vertex

the sign of a tells direction of opening